Q: Given the rate law $$\text{rate} = k[\mathrm{H_2$}]^2[\mathrm{NO}]$$ for the reaction $$2\mathrm{H_2$} + 2\mathrm{NO} \rightarrow \mathrm{N_2$} + 2\mathrm{H_2O}$$, what is the rate (in $$\mathrm{M/s}) if$$ $$k = 6.0 \times 10^4$\ \mathrm{M$$^{-2}$$s^{-2}$$}$$, $$[\mathrm{$$H_2$$}] = 0.0010\ \mathrm{M}$$, and $$[\mathrm{NO}] = 0.0020\ \mathrm{M}$?

$$1.2 \times 10$$^{-1}$$\ \mathrm{M/s}$$

Q: Using the following kinetic data for the reaction $$2\mathrm{H_2$} + 2\mathrm{NO} \rightarrow \mathrm{N_2$} + 2\mathrm{H_2O}$$: Exp 1: $$[\mathrm{NO}] = 0.0050\ \mathrm{M}$$, $$[\mathrm{H_2$}] = 0.0025\ \mathrm{M}$$, rate $$= 3.0 \times 10$$^{-3}$$\ \mathrm{M/s}$$ Exp 2: $$[\mathrm{NO}] = 0.0100\ \mathrm{M}$$, $$[\mathrm{H_2$}] = 0.0025\ \mathrm{M}$$, rate $$= 6.0 \times 10$$^{-3}$$\ \mathrm{M/s}$$ Exp 3: $$[\mathrm{NO}] = 0.0050\ \mathrm{M}$$, $$[\mathrm{H_2$}] = 0.0050\ \mathrm{M}$$, rate $$= 6.0 \times 10$$^{-3}$$\ \mathrm{M/s}$$ Exp 4: $$[\mathrm{NO}] = 0.0100\ \mathrm{M}$$, $$[\mathrm{H_2$}] = 0.0050\ \mathrm{M}$$, rate $$= 1.2 \times 10$$^{-2}$$\ \mathrm{M/s}$$ What is the correct rate law for this reaction?

$$\text{rate} = k[\mathrm{NO}]^1[\mathrm{H_2$}]^1$$

Q: The activation energy ($$E_a) of a $$reaction is $$56.8\ \mathrm{kJ/mol}$$ and the frequency factor ($$A) is$$ $$1.5 \times 10$$^{11}$$\ \mathrm{s$$^{-1}$$}. $$Calculate the rate constant ($$k) at$$ $$25^\circ\mathrm{C}$$ using the one-point Arrhenius equation. ($$R = 8.314\ \mathrm{J/(mol\cdot K)})$$

$$k = 1.5 \times 10$$^{11}$$ \exp\left(-\frac{56800}{8.314 \times 298}\right) \approx 1.1 \times 10$$^{-5}$$\ \mathrm{s$$^{-1}$$}$$

Q: A reaction has a rate constant $$k_1 = 3.20$$ \times $$10^{-5}$$\ \mathrm{$$s^{-1}$$}$$ at T_1$ = 450\ \mathrm{K}$$ and $$k_2 = 9.40$$ \times $$10^{-3}$$\ \mathrm{$$s^{-1}$$}$$ at T_2$ = 500\ \mathrm{K}. $$What is the activation energy ($$E_a) $$for this reaction? ($$R = 8.314\ \mathrm{J/(mol\cdot K)})$$

$$E_a = \frac{\ln(k_2$/k_1$)}{(1/T_1$ - 1/T_2$)} \times R \approx 110\ \mathrm{kJ/mol}$$

Q: A solution is prepared by dissolving $$0.5\ \mathrm{mol} of a $$nonvolatile solute in $$1.0\ \mathrm{kg} of $$water. If the boiling point elevation constant $$K_b$$ for water is $$0.512\ \mathrm{K\cdot kg/mol}$$, what is the boiling point elevation ($$\Delta T_b$$)? Assume $$i = 1.$$

$$\Delta T_b = i K_b m = 0.512 \times 0.5 = 0.256\ \mathrm{K}$$

Q: A gas occupies $$5.0\ \mathrm{L} at$$ $$2.0\ \mathrm{atm}$$ and $$300\ \mathrm{K}. $$How many moles of gas are present? ($$R = 0.0821\ \mathrm{L\cdot atm/(mol\cdot K)})$$

$$n = \frac{PV}{RT} = \frac{2.0 \times 5.0}{0.0821 \times 300} \approx 0.41\ \mathrm{mol}$$

Question 1

For the reaction $$\mathrm{N_2$ + 3H_2 \rightarrow 2NH_3}$$, if the average rate of consumption of $$\mathrm{H_2$} is$$ $$0.0277\ \mathrm{M/s}$$, what is the average rate of production of $$\mathrm{NH_3$}$$?

Accepted Answer

$$0.0185\ \mathrm{M/s}$$

Question 2

Given the rate law $$	ext{rate} = k[\mathrm{H_2$}]^2[\mathrm{NO}]$$ for the reaction $$2\mathrm{H_2$} + 2\mathrm{NO} ightarrow \mathrm{N_2$} + 2\mathrm{H_2O}$$, what is the rate (in $$\mathrm{M/s}) if$$ $$k = 6.0 	imes 10^4$\ \mathrm{M$$^{-2}$$s^{-2}$$}$$, $$[\mathrm{$$H_2$$}] = 0.0010\ \mathrm{M}$$, and $$[\mathrm{NO}] = 0.0020\ \mathrm{M}$?

Accepted Answer

$$1.2 	imes 10$$^{-1}$$\ \mathrm{M/s}$$

Question 3

Using the following kinetic data for the reaction $$2\mathrm{H_2$} + 2\mathrm{NO} ightarrow \mathrm{N_2$} + 2\mathrm{H_2O}$$:

Exp 1: $$[\mathrm{NO}] = 0.0050\ \mathrm{M}$$, $$[\mathrm{H_2$}] = 0.0025\ \mathrm{M}$$, rate $$= 3.0 	imes 10$$^{-3}$$\ \mathrm{M/s}$$
Exp 2: $$[\mathrm{NO}] = 0.0100\ \mathrm{M}$$, $$[\mathrm{H_2$}] = 0.0025\ \mathrm{M}$$, rate $$= 6.0 	imes 10$$^{-3}$$\ \mathrm{M/s}$$
Exp 3: $$[\mathrm{NO}] = 0.0050\ \mathrm{M}$$, $$[\mathrm{H_2$}] = 0.0050\ \mathrm{M}$$, rate $$= 6.0 	imes 10$$^{-3}$$\ \mathrm{M/s}$$
Exp 4: $$[\mathrm{NO}] = 0.0100\ \mathrm{M}$$, $$[\mathrm{H_2$}] = 0.0050\ \mathrm{M}$$, rate $$= 1.2 	imes 10$$^{-2}$$\ \mathrm{M/s}$$

What is the correct rate law for this reaction?

Accepted Answer

$$	ext{rate} = k[\mathrm{NO}]^1[\mathrm{H_2$}]^1$$

Question 4

What is the half-life ($$t_{1/2}) of a $$first-order reaction with a rate constant $$k = 0.693\ \mathrm{s$$^{-1}$$}$$?

Accepted Answer

$$t_{1/2} = \frac{0.693}{0.693} = 1\ \mathrm{s}$$

Question 5

The activation energy ($$E_a) of a $$reaction is $$56.8\ \mathrm{kJ/mol}$$ and the frequency factor ($$A) is$$ $$1.5 	imes 10$$^{11}$$\ \mathrm{s$$^{-1}$$}. $$Calculate the rate constant ($$k) at$$ $$25^\circ\mathrm{C}$$ using the one-point Arrhenius equation. ($$R = 8.314\ \mathrm{J/(mol\cdot K)})$$

Accepted Answer

$$k = 1.5 	imes 10$$^{11}$$ \exp\left(-\frac{56800}{8.314 	imes 298}ight) \approx 1.1 	imes 10$$^{-5}$$\ \mathrm{s$$^{-1}$$}$$

Question 6

A reaction has a rate constant $$k_1 = 3.20$$ 	imes $$10^{-5}$$\ \mathrm{$$s^{-1}$$}$$ at T_1$ = 450\ \mathrm{K}$$ and $$k_2 = 9.40$$ 	imes $$10^{-3}$$\ \mathrm{$$s^{-1}$$}$$ at T_2$ = 500\ \mathrm{K}. $$What is the activation energy ($$E_a) $$for this reaction? ($$R = 8.314\ \mathrm{J/(mol\cdot K)})$$

Accepted Answer

$$E_a = \frac{\ln(k_2$/k_1$)}{(1/T_1$ - 1/T_2$)} 	imes R \approx 110\ \mathrm{kJ/mol}$$

Question 7

Which equation correctly relates $$K_p$$ and $$K_c$$ for a gaseous reaction?

Accepted Answer

$$K_p = K_c(RT$$)^{\Delta n}$$

Question 8

A solution is prepared by dissolving $$0.5\ \mathrm{mol} of a $$nonvolatile solute in $$1.0\ \mathrm{kg} of $$water. If the boiling point elevation constant $$K_b$$ for water is $$0.512\ \mathrm{K\cdot kg/mol}$$, what is the boiling point elevation ($$\Delta T_b$$)? Assume $$i = 1.$$

Accepted Answer

$$\Delta T_b = i K_b m = 0.512 	imes 0.5 = 0.256\ \mathrm{K}$$

Question 9

Which of the following is the correct formula for osmotic pressure ($$\pi) of a $$dilute solution?

Accepted Answer

$$\pi = MRT$$

Question 10

A gas occupies $$5.0\ \mathrm{L} at$$ $$2.0\ \mathrm{atm}$$ and $$300\ \mathrm{K}. $$How many moles of gas are present? ($$R = 0.0821\ \mathrm{L\cdot atm/(mol\cdot K)})$$

Accepted Answer

$$n = \frac{PV}{RT} = \frac{2.0 	imes 5.0}{0.0821 	imes 300} \approx 0.41\ \mathrm{mol}$$

Question 11

If the density of water is $$1.00\ \mathrm{g/mL}$$, what is the mass of $$250\ \mathrm{mL} of $$water?

Accepted Answer

$$250\ \mathrm{g}$$

Question 12

A sample contains $$3.32 	imes 10$$^{23}$$ molecules. How many moles does this represent? (Avogadro’s number = 6.02$$ 	imes $$10^{23})$$

Accepted Answer

$$0.55\ \mathrm{mol}$$

Question 13

Which of the following correctly expresses the relationship between pressure and mole fraction in a solution?

Accepted Answer

$$P_{soln} = X_{solvent} P^0$_{solvent}$$

Question 14

A reaction is first order in $$\mathrm{A}$$ and zero order in $$\mathrm{B}. If $$the concentration of $$\mathrm{A} is $$doubled and $$\mathrm{B} is $$tripled, what happens to the rate?

Accepted Answer

The rate doubles.

Question 15

Which of the following is the correct conversion for $$1\ \mathrm{atm} to$$ $$\mathrm{Pa}$$?

Accepted Answer

$$1\ \mathrm{atm} = 101,325\ \mathrm{Pa}$$

Question 16

A reaction has a rate constant $$k$$ that increases from $$1.0 	imes 10$$^{-4}$$\ \mathrm{s$$^{-1}$$} to$$ $$1.0 	imes 10$$^{-2}$$\ \mathrm{s$$^{-1}$$}$$ when the temperature increases from $$300\ \mathrm{K} to$$ $$350\ \mathrm{K}. $$Which equation would you use to calculate the activation energy ($$E_a$$)?

Accepted Answer

$$\ln\left(\frac{k_2$}{k_1$}\right) = \frac{E_a}{R}\left(\frac{1}{T_1$} - \frac{1}{T_2$}\right)$$

Question 17

If a reaction has a rate law $$	ext{rate} = k[\mathrm{A}]^2[\mathrm{B}]$$, what is the overall order of the reaction?

Accepted Answer

Third order

Question 18

A $$1.0\ \mathrm{mol}$$ sample of an ideal gas at STP occupies what volume?

Accepted Answer

$$22.4\ \mathrm{L}$$

Question 19

Which of the following is the correct formula for freezing point depression ($$\Delta T_f$$)?

Accepted Answer

$$\Delta T_f = i K_f m$$

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