Q: What is the density of dinitrogen monoxide (N$$_2O) at $$STP?

$$\text{Density} = \frac{\text{Molar mass}}{22.4\ \text{L}} = \frac{44.0\ \text{g/mol}}{22.4\ \text{L}} = 1.96\ \text{g/L}$$

Q: What is the relative rate of diffusion of nitrogen gas (N$$_2) $$and argon (Ar)?

$$\text{Rate}_{N_2$}/\text{Rate}_{Ar} = \sqrt{\frac{M_{Ar}}{M_{N_2$}}} = \sqrt{\frac{39.95}{28.02}} = 1.19$$

Q: How many moles of gas will occupy 20.0 L at 0.990 atm and 15.7 \degree C?

$$n = \frac{PV}{RT} = \frac{0.990 \times 20.0}{0.08206 \times 288.85} = 0.85$$ mol

Q: What is the molecular mass of a gas with a density of 1.16 g/L at STP?

$$\text{Molar mass} = \text{Density} \times 22.4 = 1.16 \times 22.4 = 26.0 g/$$mol

Question 1

A 5.00 L sample of a gas exerts a pressure of 750 torr. What pressure will result if the volume is changed to 4.20 L, assuming temperature and amount of gas remain constant?

Accepted Answer

$$P_1$$ $$V_1$$ = $$P_2$$ $$V_2$$; $$P_2$$ = \frac{$$P_1$$ $$V_1$$}{$$V_2$$} = \frac{750 	imes 5.00}{4.20} = 893$$ torr

Question 2

A 5.00 L sample of a gas at 75.0 \degree C is cooled to 15.0 \degree C. What is the new volume, assuming pressure and amount of gas remain constant?

Accepted Answer

$$\frac{V_1$}{T_1$} = \frac{V_2$}{T_2$}$$; $$V_2$$ = $$V_1$$ 	imes \frac{$$T_2$$}{$$T_1$$} = 5.00 	imes \frac{288.15}{348.15} = 4.14$$ L

Question 3

A sample of a gas at 755 torr is heated from 18.0 \degree C to 45.0 \degree C. What is the new pressure, assuming volume and amount of gas remain constant?

Accepted Answer

$$\frac{P_1$}{T_1$} = \frac{P_2$}{T_2$}$$; $$P_2$$ = $$P_1$$ 	imes \frac{$$T_2$$}{$$T_1$$} = 755 	imes \frac{318.15}{291.15} = 825$$ torr

Question 4

Which statement best describes Boyle's Law?

Accepted Answer

At constant temperature, the pressure of a gas is inversely proportional to its volume: $$P \propto \frac{1}{V}$$

Question 5

According to Gay-Lussac's Law, what happens to the pressure of a gas if its temperature increases at constant volume?

Accepted Answer

The pressure increases proportionally with temperature: $$P \propto T$$

Question 6

A 1.00 L sample of a gas at STP is heated to 55.0 \degree C. If the pressure increases to 800 torr, what is the new volume?

Accepted Answer

$$\frac{P_1$ V_1$}{T_1$} = \frac{P_2$ V_2$}{T_2$}$$; $$V_2$$ = \frac{$$P_1$$ $$V_1$$ $$T_2$$}{$$P_2$$ $$T_1$$} = \frac{1.00 	imes 273.15 	imes 800}{760 	imes 328.15} = 0.89$$ L

Question 7

For the following reaction, if 10.0 L of nitrogen gas react, what volume of ammonia gas is produced? $$N_2 + 3H_2$$ \rightarrow 2NH_3$$ (Assume all gases are measured at the same temperature and pressure.)

Accepted Answer

20.0 L of ammonia gas

Question 8

What is the density of dinitrogen monoxide (N$$_2O) at $$STP?

Accepted Answer

$$	ext{Density} = \frac{	ext{Molar mass}}{22.4\ 	ext{L}} = \frac{44.0\ 	ext{g/mol}}{22.4\ 	ext{L}} = 1.96\ 	ext{g/L}$$

Question 9

What is the relative rate of diffusion of nitrogen gas (N$$_2) $$and argon (Ar)?

Accepted Answer

$$	ext{Rate}_{N_2$}/	ext{Rate}_{Ar} = \sqrt{\frac{M_{Ar}}{M_{N_2$}}} = \sqrt{\frac{39.95}{28.02}} = 1.19$$

Question 10

How many moles of gas will occupy 20.0 L at 0.990 atm and 15.7 \degree C?

Accepted Answer

$$n = \frac{PV}{RT} = \frac{0.990 	imes 20.0}{0.08206 	imes 288.85} = 0.85$$ mol

Question 11

What is the molecular mass of a gas with a density of 1.16 g/L at STP?

Accepted Answer

$$	ext{Molar mass} = 	ext{Density} 	imes 22.4 = 1.16 	imes 22.4 = 26.0 g/$$mol

Question 12

Nitrogen gas is produced by the decomposition of sodium azide. If 223 mL of nitrogen are produced at 755 torr and 21.9 \degree C, what is the mass of nitrogen gas generated?

Accepted Answer

$$n = \frac{PV}{RT} = \frac{0.993 	imes 0.223}{0.08206 	imes 295.05} = 0.0092$$ mol; $$m = n 	imes 28.02 = 0.26 g$$

Question 13

Calculate $$\Delta H$$ for the reaction $$2NOCl_{(g)} \rightarrow 2NO_{(g)} + Cl_{2(g)}$$ using the following data: $$NO_{(g)} + \frac{1}{2}Cl_{2(g)} \rightarrow NOCl_{(g)}$$, $$\Delta H = -38.6 kJ$$; $$NO_{(g)} + \frac{1}{2}O_{2(g)} \rightarrow NO_{2(g)}$$, $$\Delta H = -33.1 kJ.$$

Accepted Answer

$$\Delta H = +77.2 kJ$$

Question 14

Given the standard enthalpies of formation: $$\Delta H_f$$^{\circ}$$($$MgCO_3$$) = -1095.8 kJ/$$mol, $$\Delta H_f$$^{\circ}$$(MgO) = -601.6 kJ/$$mol, $$\Delta H_f$$^{\circ}$$(CO_2$) = -393.5 kJ/$$mol, calculate $$\Delta H$$ for the reaction $$MgCO_3$$ \rightarrow MgO + $$CO_2.$$

Accepted Answer

$$\Delta H = [(-601.6) + (-393.5)] - (-1095.8) = 100.7 kJ$$

Question 15

A solution is prepared by mixing 50.0 mL of 0.100 M AgNO$$_3$$ and 50.0 mL of 0.100 M HCl. A precipitate of AgCl is formed. Given the specific heat of water $$4.18\ 	ext{J/g}\cdot\degree	ext{C}$$ and final temperature of 22.40 \degree C, initial temperature 21.40 \degree C, calculate $$\Delta H of $$the reaction per mole AgCl formed.

Accepted Answer

$$q = m c \Delta T = 100 	imes 4.18 	imes (22.40 - 21.40) = 418 J$$; 	ext{Moles AgCl} = 0.0050$$; $$\Delta H = \frac{418}{0.0050} = 83,600$$ J/mol = 83.6$ kJ/mol

Question 16

Combustion of one mole of propylene (C$$_3H$_6) $$yields 2053 kJ/mol. If 43.5 g of propylene are burned in a bomb calorimeter with a heat capacity of 6.70 kJ/\degree C, what will be the change in temperature?

Accepted Answer

$$n = \frac{43.5}{42.08} = 1.03$$ mol; $$q = 1.03 	imes 2053 = 2114 kJ$$; $$\Delta T = \frac{2114}{6.70} = 316$$ \degree C

Question 17

Estimate the enthalpy of this reaction from the bond energies: $$CH_3OH \rightarrow CH_2O + H_2$. Given: C-H = 413 kJ/mol, C-O = 358 kJ/mol, O-H = 464 kJ/mol, H-H = 436 kJ/mol.

Accepted Answer

$$\Delta H = 	ext{Bonds broken} - 	ext{Bonds formed} = [3 	imes 413 + 358 + 464] - [2 	imes 413 + 358 + 436] = 2061 - 1620 = 441 kJ/$$mol

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