A tractor collides with a car while driving down the road. The car travels at a speed of 25m/s and weighs 1,300 kg. What is the momentum of the car? If the tractor weighs 1,500 kg and traveled at 5 m/s what was the total momentum of the collision?

Answers

Answer 1

The momentum of the car is 32,500 kg m/s, and the total momentum of the collision is 40,000 kg m/s.

The momentum of an object is calculated by multiplying its mass by its velocity. In the case of the car, its mass is 1,300 kg, and it travels at a speed of 25 m/s. To find the car's momentum, we can use the formula:

momentum = mass × velocity

Car's momentum = 1,300 kg × 25 m/s = 32,500 kg m/s

Now, let's find the momentum of the tractor. The tractor weighs 1,500 kg and travels at 5 m/s. Using the same formula:

Tractor's momentum = 1,500 kg × 5 m/s = 7,500 kg m/s

To find the total momentum of the collision, we simply add the momentum of the car and the tractor:

Total momentum = Car's momentum + Tractor's momentum
Total momentum = 32,500 kg m/s + 7,500 kg m/s = 40,000 kg m/s

In conclusion, the momentum of the car is 32,500 kg m/s, and the total momentum of the collision is 40,000 kg m/s.

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Related Questions

Alcohols are flammable, suggest how the mixture of alcohols should be safely heated so that ethanol can be collected

Answers

liquid ethanol can be separated from a mixture of ethanol and water by fractional distillation. This method works because the liquids in the mixture have different boiling points. When the mixture is heated, one liquid evaporates before the other.

WHAT IS IT I NEED HELP PLS HELP

WHAT IS IT I NEED HELP PLS HELP

Answers

The cells as observed by Andrea could have been growing to their full sizes as at the time they were collected. Option B.

The Interphase

The interphase is one of the major phases in the life cycle of a living cell. The phase is characterized by a host of cellular activities which happen at sub-phase levels.

These sub-phases and their activities include:

G1 phase: a phase that is largely characterized by cell growth and development.S phase: a phase during which the DNA of cells is synthesized.G2 phase: a phase that has to do with protein and hormone synthesis.

According to Andrea's observation via the microscope, the cells are in interphase. Thus, the observed cells could have been growing to their full sizes as at the time they were collected.

This is because cells growing to their full sizes is one of the activities that happen at the interphase, the G1 phase to be precise.

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How many milliliters of 0. 250M NaOH is required to neutralize 30. 4mL of 0. 152M HCl?

Answers

Approximately 18.4832 mL of 0.250 M NaOH is required to neutralize 30.4 mL of 0.152 M HCl.

To determine the volume of 0.250 M NaOH required to neutralize 30.4 mL of 0.152 M HCl, we can use the concept of stoichiometry and the balanced chemical equation for the neutralization reaction between NaOH and HCl:

NaOH + HCl -> NaCl + H2O

From the balanced equation, we can see that the stoichiometric ratio between NaOH and HCl is 1:1. This means that for every mole of NaOH, we require an equal number of moles of HCl to neutralize.

First, let's calculate the number of moles of HCl present in the given volume:

Moles of HCl = concentration of HCl * volume of HCl

= 0.152 M * 30.4 mL

= 4.6208 mmol (millimoles)

Since the stoichiometric ratio is 1:1, the number of moles of NaOH required to neutralize the HCl is also 4.6208 mmol.

Now, let's calculate the volume of 0.250 M NaOH needed to contain 4.6208 mmol:

Volume of NaOH = (moles of NaOH) / (concentration of NaOH)

= 4.6208 mmol / 0.250 M

= 18.4832 mL

Therefore, approximately 18.4832 mL of 0.250 M NaOH is required to neutralize 30.4 mL of 0.152 M HCl.

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In which container are the particles of water moving fastest? In which container are the particles moving slowest

Answers

Answer:

Particles move faster the farther they are apart, so the container with the most spread out particles.

What will most likely happen to the Sun in the future?
A. The Sun will burn away most of its fuel and become a red giant star.
B. The Sun will collapse and become a large planet like Jupiter.
C. The Sun will become a giant collection of gas and dust called a nebula
D. The Sun will cool to become a blue dwarf.

Answers

Answer:

b

Explanation:

because the sun it's already the biggest planet

How many moles of water are produced from the reaction of oxygen with four moles of propane (C3H8)? C3H8 + 5O2 --> 3CO2 + 4H2O

Answers

Answer:

Explanation:

The reaction is:

C₃H₈ + 5O₂  →  3CO₂  +  4H₂O

We see, that the equation is ballanced.

As we have data from only one reactant, we assume the other is in excess.

Ratio is 1:4 (stoichiometry). We solve this, by a rule of three:

1 mol of propane can produce 4 moles of water

Then, 4 moles of propane, may produce

( 4 . 4 ) /1 = 16 moles of water can be made.

Remember, we always have to work with the limiting reactant.

How do you write a nuclear equation in chemistry?

Answers

To write a nuclear equation in chemistry, identify the isotopes involved, write the reactants and products, and balance the equation to conserve mass and atomic numbers. Indicate any emission or absorption of particles using appropriate superscripts or subscripts.

We can also follow these steps;

1. Identify the isotopes involved: Determine the atomic symbols and atomic numbers of the isotopes participating in the nuclear reaction.

2. Write the reactants and products: Place the reactant isotopes on the left side of the equation and the product isotopes on the right side. Separate them with an arrow.

3. Balance the equation: Ensure that the total mass number and atomic number are conserved on both sides of the equation.

Adjust the coefficients (numbers in front of the isotopes) as needed to balance the equation.

4. Indicate emission or absorption: If there is emission of particles such as alpha particles (α), beta particles (β), or gamma radiation (γ), write them as superscripts or subscripts after the isotopes involved.Here's an example of a nuclear equation for the alpha decay of uranium-238:

^238U → ^234Th + ^4He

In this example, uranium-238 (U-238) undergoes alpha decay, resulting in the formation of thorium-234 (Th-234) and the emission of an alpha particle (helium-4, He-4).

Remember that nuclear equations represent the changes occurring in the atomic nucleus during nuclear reactions, which involve the rearrangement of protons and neutrons.

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Why is the 6 m naoh solution diluted before titrating the vinegar sample? How might your results be affected if you used the 6 m solution rather than the 0. 3 m naoh?

Answers

The 6 M solution NaOH solution diluted before titrating the vinegar sample because pH at the equivalence point changes very rapidly . It is very useful to have dilution solution , so that number of moles that are transferred per drop of the solution is low . So, pH change smaller amount per drop. Having more dilute solution also allows the titration to use volume that is easier to work with.

If you used the 6 M solution was used then the volume required for titration would go down by a factor of 6/0.3 = 20

This means that if a titration took 20ml of the 0.3 M solution then it would take 1ml of the NaOH solution.

Titration consists of adding a controlled and known amount of standard solution with an unknown until the reaction to be complete.

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What is the purpose of a catalyst in the production of hydrogen?
Select the correct answer.
- to increase the rate at which water molecules decompose
- to decrease the amount of oxygen produced
- to decrease the temperature of the reaction
- to increase the activation energy of the reaction

Answers

The purpose of a catalyst in the production of hydrogen is to increase the rate at which water molecules decompose.

What is a catalyst-A catalyst is a substance that increases the rate of a chemical reaction without itself being consumed or produced during the reaction. As a result, catalysts assist in speeding up chemical reactions while also decreasing the amount of energy needed for the reaction to occur. In hydrogen production, catalysts are used to speed up the decomposition of water into hydrogen and oxygen. The use of catalysts lowers the activation energy required for the reaction to occur, resulting in a faster reaction rate and lower operating temperatures.What is the process of hydrogen production?Hydrogen production has various methods, and one of the most commonly used methods is water electrolysis. In this method, water molecules are split into hydrogen and oxygen using an electric current passed through an electrode. Water is broken down into hydrogen and oxygen during the process, with the assistance of a catalyst. During this process, a catalyst like platinum or nickel is employed to speed up the chemical reaction of water decomposition.

When an electric current is applied to the catalyst, water molecules are broken apart, releasing hydrogen and oxygen atoms.Catalysts lower the activation energy of the reaction, allowing it to occur faster than it would otherwise. In hydrogen production, catalysts are crucial since they enable the reaction to occur at a lower temperature, reducing energy consumption and minimizing operating costs. As a result, the use of catalysts is essential to the production of hydrogen.

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How is thermal energy distributed in most heating systems?

A.
convection

B.
conduction

C.
radiation

Answers

Answer:

By Convection

Explanation:

what is the volume of the rock with a density of 3.5 g/cm
3
and a mass of 77 g?

Answers

Explanation:

Density = mass/volume

.: volume = mass/density

Volume = 77/3.5

Volume = 22cm³

Epinephrine (adrenaline) is a hormone secreted into the bloodstream in times of stress. It contains 59.0% C, 7.15% H, 26.20% O, and 7.65% N and has a molar mass of 183 g/mol. What is its molecular formula

Answers

Answer:

C9H13O3N

Explanation:

Take the atomic mass of C=12.0, H=1.0, O=16.0 and N=14.0.

We can draw a chart (please view this on desktop so to avoid spacing errors):

Let the mass of Epinephrine be 100g.

                             C                       H                          O                              N

mass(g) :              59                      7.15                    26.2                         7.65

no. of moles : 59/12 =4.9167     7.15/1 = 7.15     26.2/16=1.6375 7.65/14=0.5464

(n.o.m. = mass/molar mass)

Ratio:   4.9167/0.5464 =9    7.15/0.5464=13      1.6375= 3      0.5464/0.5464 =1

(divide the n.o.m. by the smallest n.o.m., which is 0.5464 in this case, take the whole numbers)

So, the empirical formula will be: C9H13O3N

But this is still not yet the molecular formula. We have to ensure the molar mass is 183g/mol. Multiply the empirical formula by n.

So, let the molecular formula of Epinephrine be (C9H13O3N)n.

12x9n + 1x13n + 16x3n + 14n = 183

108n + 13n + 48n + 14n = 183

183 n = 183.

n = 1

Hence, the molecular formula is C9H13O3N.

what force other than the ionic concentration gradieent determines the lectrical. potential difference sodium potassium. pump electrical. resistance electrical conductance electrical current

Answers

The force other than the ionic concentration gradient that determines the electrical potential difference in the sodium-potassium pump is the electrical charge difference across the membrane. This is also known as the membrane potential.

The sodium-potassium pump is a type of active transport that moves sodium ions out of the cell and potassium ions into the cell. This creates an ionic concentration gradient, with a higher concentration of sodium ions outside the cell and a higher concentration of potassium ions inside the cell. This gradient is one of the forces that determines the electrical potential difference across the membrane.

However, another important force is the electrical charge difference across the membrane. The sodium-potassium pump moves three sodium ions out of the cell for every two potassium ions it moves in. This creates a net charge difference, with more positive charges outside the cell and more negative charges inside the cell. This charge difference contributes to the membrane potential and is another important factor in determining the electrical potential difference across the membrane.

In summary, both the ionic concentration gradient and the electrical charge difference across the membrane determine the electrical potential difference in the sodium-potassium pump.

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What does this diagram represent? (4 points) A glycerol molecule losing an H atom, and a fatty acid chain losing OH, forming H2O. 1. A saturated fat becoming unsaturated 2. A fat molecule forming through dehydration synthesis 3. The saturation of a triglyceride molecule 4. Dehydration synthesis breaking down a fat molecule

Answers

Answer:

This question is incomplete because of the absence of the diagram

Explanation:

The absence of the diagram makes the question incomplete, but it appears as if the content of the diagram has been described in the question (which is not totally clear).

The description provided in the question suggests the loss of a water during the formation of a triglyceride. This process described here is called dehydration synthesis. Dehydration synthesis is the process of joining two substances/compounds together leading to the loss of water molecule in the process.

From the explanation above, the correct option is 2. The fat molecule being formed is the triglyceride (through the process of dehydration synthesis).

Make the following conversions:
1.1.51 x 1015 atoms Si to mol Si

Answers

Answer:

2.52x10^-9 mol

Explanation:

A student has a sample of 1.58 moles of fluorine gas that is contained in a 25.3 L container at 274 K. What is the pressure of the sample? The ideal gas constant is 0.0821 L*atm/mol*K. Round your answer to the nearest 0.01 and include units.

(please hurry)!! and thank you in advance.

Answers

The pressure of the sample is  1.74 atm.

What is pressure?

Pressure is described as  the force applied perpendicular to the surface of an object per unit area over which that force is distributed.

We make use of the ideal gas law equation:

PV = nRT

where:

P = pressure

V = volume

n = moles

R = ideal gas constant

T = temperature

Note that the ideal gas law states that the volume of a given amount of gas is directly proportional to the number on moles of gas, directly proportional to the temperature and inversely proportional to the pressure.

We then substitute the  values into the equation:

P * 25.3 = 1.58 * 0.0821 * 274

pressure = (1.58 * 0.0821 * 274) / 25.3

pressure= 1.7378 atm

pressure  = 1.74 atm.

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Dr. Laude doesn’t care for fancy definitions of a mole. He prefers the idea that a mole is:

A) an amount of a substance you can hold in your hand.
B) the amount of a substance you can store in a shoebox.
C) the amount of a substance you can place on the head of a pin.
D) the amount of a substance you can see with a microscope.

Answers

Answer:

A

Explanation:

Dr. Laude  prefers the idea that a mole is an amount of a substance you can hold in your hand.

What is a mole?

Mole is defined as the unit of amount of substance . It is the quantity measure of amount of substance of how many elementary particles are present in a given substance.

It is defined as exactly 6.022×10²³ elementary entities. The elementary entity can be a molecule, atom ion depending on the type of substance. Amount of elementary entities in a mole is called as Avogadro's number.

It is widely used in chemistry as a suitable way for expressing amounts of reactants and products.For the practical purposes, mass of one mole of compound in grams is approximately equal to mass of one molecule of compound measured in Daltons .Molar mass has units of gram per mole . In case of molecules, where molar mass  in grams present in one mole  of atoms is its atomic mass.

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ionic bond formation by correctly pairing these terms: cation, anion, electron gain, and electron loss.

Answers

Answer:

cation - electron loss hence positive charge

anion - electron gain hence negative charge

The given terms are correctly paired thus: anion is to electron gain while cation is to electron loss.

What is ionic bond formation?

Ionic bond formation is defined as the formation of an ionic bond during a chemical reaction whereby an atom losses electrons while another gains electrons through transfer of these electrons.

For example in the formation of the compound NaCl. Sodium is the element that donates an electron from its outermost shell to chloride. Therefore, the sodium atom is the cation.

Also the chloride element would accept electron from the sodium, therefore, it is called the anion.

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Acceleration due to gravity is ___meters per second squared.

Answers

Answer:

Thus, the Earth's gravitational field (near ground level) can be quoted as 9.8 metres per second squared, or the equivalent 9.8 N/kg. Acceleration can be measured in ratios to gravity, such as g-force, and peak ground acceleration in earthquakes.

Explanation:

Andrew and Sullivan were arguing over bond lengths. Andrew said that F-CI has a shorter bond
length than F-H because F and Cl have greater electronegativity and therefore form a shorter
bond. Sullivan disagrees, stating that electronegativity has nothing to do with bond length.
Who's right? Why?

Answers

The ability of an atom to draw in the shared pair of electrons is measured by its electronegativity. For calculating electronegativity, people frequently utilize the Pauling scale.

What is electronegativity?

When an electron is added to a neutral atom in a gaseous state to create a negative ion, the energy of the atom changes (in units of kJ/mole). In essence, it conveys the atom's propensity to pick up an electron.

In the modern periodic table's 17th group, fluorine is located above chlorine. Despite having seven electrons in its valence shell, it is smaller than an atom of chlorine.

The electron density rises as a result. Fluorine has a higher electronegativity because of its high electron density, which can draw in a shared pair of electrons.

Therefore, The ability of an atom to draw in the shared pair of electrons is measured by its electronegativity. For calculating electronegativity, people frequently utilize the Pauling scale.

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A certain first-order reaction a → b is 25% complete in 42 min at 25°c. What is the half-life of the reaction?.

Answers

The half-life of the reaction is 101.9 min

First order reaction

When a reaction's pace and reactant concentration are inversely correlated, the process is known as a first-order reaction. To put it another way, the reaction rate doubles when the concentration does. One or two reactants can be present in a first-order reaction, as in the case of the decomposition process.

The half-life of first-order reaction:-

The amount of time it takes for the initial concentration of the reactant(s) to decrease by half is known as the half-life of a chemical reaction (abbreviated as "t1/2").

Calculation:-

a→b

25% reacted means 75% remains

t=42 min

Rate constant

k=(2.303/t)(log a/a-x)

k=(2.303/42)(log 100/100-25 )

k=(0.054) (log 100/75)

k=(0.054)(0.1249)

k=0.0068 per min

half life

t1/2=(0.693/k)

     =(0.693/0.0068)

     =101.9 min

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The process by which heated, or hot liquid rises, cools, and then sinks is called

Answers

The process by which heated, or hot liquid rises, cools, and then sinks is called convection.

Convection is the process by which heated, or hot liquid rises, cools, and then sinks. Convection currents are also responsible for the circulation of air in the atmosphere and the flow of currents in the ocean. In fluid dynamics, the term "convection" refers to the movement of heat or mass as a result of the collective motion of molecules within fluids (liquids or gases).

The heat transfer is caused by a temperature difference across the fluid. Heat flows from the hot region to the cold region, resulting in fluid motion. Convection is driven by differences in temperature or density within a fluid. When a fluid is heated, it expands, becomes less dense, and rises. Cooler, denser fluid sinks to replace the rising fluid. This process results in the formation of convection currents.

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You need to prepare 100.0 mL of a pH 4.00 buffer solution using 0.100M benzoic acid (pK
a

=4.20) and 0.240M sodium benzoatc. How many milliliters of each solution should be mixed to prepare this buffer? benzoic acid:
Previous question

Answers

To prepare the pH 4.00 buffer solution, you should mix approximately 61.35 mL of the 0.100 M benzoic acid solution with 38.65 mL of the 0.240 M sodium benzoate solution.The ratio of benzoic acid to sodium benzoate in the buffer solution using the Henderson-Hasselbalch equation.

To prepare a pH 4.00 buffer solution using benzoic acid and sodium benzoate, we need to calculate the appropriate volumes of the 0.100 M benzoic acid and 0.240 M sodium benzoate solutions.

First, we need to determine the ratio of benzoic acid to sodium benzoate in the buffer solution. The Henderson-Hasselbalch equation can help us with this calculation:

pH = pKa + log([A-]/[HA])

Given that the pH is 4.00 and pKa is 4.20, we can rearrange the equation:

log([A-]/[HA]) = pH - pKa

log([A-]/[HA]) = 4.00 - 4.20

log([A-]/[HA]) = -0.20

Next, we take the antilog of -0.20 to find the ratio of [A-] to [HA]:

[A-]/[HA] = antilog(-0.20)

[A-]/[HA] = 0.63

The ratio of [A-] to [HA] is 0.63.

Now, let's calculate the volumes of each solution needed. Let's assume x represents the volume (in mL) of the 0.100 M benzoic acid solution and y represents the volume (in mL) of the 0.240 M sodium benzoate solution.

Since the total volume is 100.0 mL, we have the equation: x + y = 100

Considering the ratio of [A-] to [HA] as 0.63, we can write the equation: y/x = 0.63

Solving these two equations simultaneously will give us the volumes of each solution:

x + y = 100

y/x = 0.63

By substituting y = 0.63x from the second equation into the first equation, we get:

x + 0.63x = 100

1.63x = 100

x = 61.35 mL (rounded to two decimal places)

Substituting this value back into the equation x + y = 100, we find:

61.35 + y = 100

y = 38.65 mL (rounded to two decimal places)

Therefore, to prepare the pH 4.00 buffer solution, you should mix approximately 61.35 mL of the 0.100 M benzoic acid solution with 38.65 mL of the 0.240 M sodium benzoate solution.

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2)
Compare the atomic radius of an atom of bromine to the atomic radius of an atom
potassium when both atoms are in the ground state.

Answers

Potassium and the atoms is right have a good day

suppose 65.0 j of heat are added to a 105 g piece of aluminum at 22.0 ∘c.

Answers

Given the heat added (Q) and the mass (m) of the aluminum piece, we can calculate the change in temperature (ΔT) using the equation:

ΔT = Q / (c * m)

where c is the specific heat capacity of aluminum, which is approximately 0.90 J/g°C.

Plugging in the values:

ΔT = 65.0 J / (0.90 J/g°C * 105 g) = 65.0 J / 95.5 J/°C = 0.68°C

So the temperature of the aluminum piece would increase by 0.68°C to 22.68°C

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Aluminum hydroxide dissolves in strong acid by the following reaction. Al(OH)3(s) + 3 H3O+(aq) equilibrium reaction arrow Al3+ (aq) + 6 H2O(l) (a) What is the equilibrium constant expression for the reaction?

Answers

The equilibrium constant expression for the reaction is: Kc = [Al3+][H2O]^6 /[H3O+]^3[Al(OH)3]

Equilibrium constant expression

The equilibrium constant expression is a mathematical expression that shows the relationship between the concentrations of reactants and products at equilibrium. In the given equation, the equilibrium constant expression would be:

Kc = [Al3+][H2O]^6 / [H3O+]^3[Al(OH)3]

where [ ] represents the concentration of the respective species in moles per liter (M).

The expression shows that at equilibrium, the ratio of the concentrations of the products to the concentrations of the reactants is constant, and this constant is defined as the equilibrium constant (Kc).

The value of Kc for a given reaction is determined by the nature of the reactants and products and the temperature at which the reaction takes place.

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How much tin II fluoride will be made when reacting 45.0 grams of tin with an excess of hydrofluoric acid if the percent yield for the reaction is 60%

Sn + HF = SnF2 + H2

Answers

Mass of SnF₂ produced : 35.634 g

Further explanation

Reaction

Sn+2HF⇒SnF₂+H₂

mol Sn (Ar 118.710 g/mol) :

\(\tt \dfrac{45}{118.710}=0.379\)

mol SnF₂ = mol Sn = 0.379

mass SnF₂ (MW=156.69 g/mol) :

\(\tt 0.379\times 156.69=59.39~g\)⇒theoretical

\(\tt \%yield=\dfrac{actual}{theoretical}\times 100\%\\\\60\%=\dfrac{actual}{59.39}\times 100\%\\\\actual=0.6\times 59.39=35.634~g\)

What is the pH and final composition of the resulting solution if it contains 10-2 M of both NH4Cl and NaHS

Answers

The final composition of the resulting solution of 10^-2 M NH4Cl and NaHS will have a pH of 9.36.

We are given the concentration of NH4Cl and NaHS as 10^-2 M.The ammonium ion (NH4+) will undergo hydrolysis in water and form NH3 and H+.NH4+ + H2O ⇌ NH3 + H+ (acid-base reaction)The reaction shows that the ammonium ion is an acid and will produce hydrogen ions in an aqueous solution.On the other hand, sodium hydrogen sulfide (NaHS) is a weak base and undergoes hydrolysis in an aqueous solution.NaHS + H2O ⇌ NaOH + H2SThe equation shows that hydrogen sulfide (HS-) is a weak acid and will produce hydroxide ions in an aqueous solution.The hydrolysis reactions of the two salts lead to an increase in hydroxide ions (OH-) in the solution, leading to a basic solution.

We can calculate the pH of the solution using the Kb values of NaHS and the Ka value of NH4+.NH4+ + H2O ⇌ NH3 + H+Ka = [NH3][H+]/[NH4+]Kb = [HS-][OH-]/[NaHS]We can assume the concentrations of NH3 and HS- to be the same, let's assume it is x, then the equilibrium constant can be expressed as:Kw = Ka × Kb[H+][OH-] = Ka × Kb[H+][OH-] = (1.8 × 10^-5) × (1.2 × 10^-13) = 2.16 × 10^-18pH + pOH = 14pH + pOH = 14pH = 14 - pOHpOH = -log[OH-] = -log(1.47 × 10^-8) = 7.83pH = 14 - 7.83 = 6.17We can conclude that the pH of the resulting solution will be 9.36 and the final composition of the resulting solution of 10^-2 M NH4Cl and NaHS will be basic.

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An object was measured by a worker as 35.6 cm long, however, the manufacturer specifications list the length of the object at 35.0 cm. What is the percent error in the workers measurement?

Answers

The answer for this question is 1.71%

Rieun pours 377 g of water at 54°C into an 816-g aluminum container with an initial temperature of 12°C. The specific heat of aluminum is 900 J/(kg ∙ K) and that of water is 4190 J/(kg ∙ K). Assuming no heat is exchanged with the surroundings, find the final temperature of the system in celsius degrees. Please give your answer with one decimal place.

Answers

Answer:

The final temperature of the system, with one decimal place, is 29.5°C.

Explanation:

The heat gained by the aluminum container will be equal to the heat lost by the water. We can use the equation:

Q_aluminum = Q_water

where Q_aluminum is the heat gained by the aluminum container, and Q_water is the heat lost by the water.

The heat gained by the aluminum container can be calculated using the specific heat of aluminum, the mass of the container, and the change in temperature:

Q_aluminum = (mass_aluminum) x (specific_heat_aluminum) x (change in temperature)

Q_aluminum = (816 g) x (0.9 J/(g∙K)) x (final temperature - 12°C)

The heat lost by the water can be calculated using the specific heat of water, the mass of the water, and the change in temperature:

Q_water = (mass_water) x (specific_heat_water) x (change in temperature)

Q_water = (377 g) x (4,190 J/(g∙K)) x (54°C - final temperature)

Since Q_aluminum = Q_water, we can set these two equations equal to each other and solve for the final temperature:

(mass_aluminum) x (specific_heat_aluminum) x (final temperature - 12°C) = (mass_water) x (specific_heat_water) x (54°C - final temperature)

(816 g) x (0.9 J/(g∙K)) x (final temperature - 12°C) = (377 g) x (4,190 J/(g∙K)) x (54°C - final temperature)

Simplifying and solving for final temperature, we get:

final temperature = 29.5°C

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