General Chemistry Exam 3 Review – Step-by-Step Study Guidance

Q1. If 10 g of sodium bicarbonate (NaHCO3) is combined with an excess of hydrochloric acid (HCl), how many liters of carbon dioxide (CO2) gas are produced at 1.0 atm and 20 °C?

Background

Topic: Stoichiometry and Gas Laws

This question tests your ability to use stoichiometry to determine the amount of gas produced in a chemical reaction, and then apply the ideal gas law to find the volume of gas at given conditions.

Key Terms and Formulas:

• Molar mass: The mass of one mole of a substance (g/mol).

• Ideal Gas Law: $PV = nRT$

• Where:

  • $P$ = pressure (atm)

  • $V$ = volume (L)

  • $n$ = moles of gas

  • $R$ = ideal gas constant ($0.0821$ L·atm/mol·K)

  • $T$ = temperature (K)

Step-by-Step Guidance

1. Write the balanced chemical equation:

   $\mathrm{NaHCO_3 (s) + HCl (aq) \rightarrow CO_2 (g) + H_2O (l) + NaCl (aq)}$

2. Calculate the number of moles of NaHCO3 used:

   $\text{Moles of NaHCO}_3 = \frac{10\ \mathrm{g}}{84.01\ \mathrm{g/mol}}$

3. From the balanced equation, determine the moles of CO2 produced (1:1 ratio with NaHCO3):

   $\text{Moles of CO}_2 = \text{Moles of NaHCO}_3$

4. Convert the temperature to Kelvin:

   $T = 20\ ^\circ\mathrm{C} + 273.15 = 293.15\ \mathrm{K}$

5. Set up the ideal gas law to solve for volume:

   $V = \frac{nRT}{P}$

Try solving on your own before revealing the answer!

Final Answer: 2.9 L

Using $n = 0.119$ mol, $R = 0.0821$ L·atm/mol·K, $T = 293.15$ K, and $P = 1.0$ atm:

$V = \frac{(0.119)(0.0821)(293.15)}{1.0} \approx 2.9$ L

The calculation shows the correct use of stoichiometry and the ideal gas law to find the volume of CO2 produced.

Q2. What are the three principles of kinetic molecular theory?

Background

Topic: Kinetic Molecular Theory of Gases

This question tests your understanding of the basic postulates that describe the behavior of ideal gases at the molecular level.

Key Terms:

• Kinetic Molecular Theory: A model that explains the physical properties of gases based on the motion of their particles.

• Elastic collisions: Collisions in which no kinetic energy is lost.

Step-by-Step Guidance

1. Recall that the theory describes gas particles as being in constant, random motion.

2. Think about the size of gas particles compared to the space between them.

3. Consider how temperature affects the motion of gas particles.

4. Remember what happens when gas particles collide with each other or with the walls of the container.

Try summarizing the three principles before checking the answer!

Final Answer:

1. Gas particles are very small compared to the distances between them.

2. Particle velocity (kinetic energy) is proportional to temperature in Kelvin.

3. Collisions between particles and with the container walls are perfectly elastic.

Q3. What is pressure?

Background

Topic: Gas Properties

This question tests your understanding of the physical meaning and units of pressure.

Key Terms and Formulas:

• Pressure ($P$): Force per unit area.

• Formula: $P = \frac{F}{A}$

• Common units: atm, Pa, psi, torr

Step-by-Step Guidance

1. Recall that pressure is defined as the amount of force applied over a specific area.

2. Think about how this applies to gases in a container (collisions with the walls).

3. Remember the common units used to measure pressure (atmospheres, pascals, psi, etc.).

Try defining pressure in your own words before checking the answer!

Final Answer:

Pressure is force per unit area, or literally pounds per square inch (psi).

Q4. Rationalize Boyle’s Law, Charles’s Law, Avogadro’s Law, and Dalton’s Law according to kinetic molecular theory.

Background

Topic: Gas Laws and Kinetic Molecular Theory

This question asks you to connect the macroscopic gas laws to the microscopic behavior of gas particles as described by kinetic molecular theory.

Key Terms:

• Boyle’s Law: $P \propto \frac{1}{V}$ (at constant $n$ and $T$)

• Charles’s Law: $V \propto T$ (at constant $n$ and $P$)

• Avogadro’s Law: $V \propto n$ (at constant $P$ and $T$)

• Dalton’s Law: $P_{\text{total}} = \sum P_i$

Step-by-Step Guidance

1. For each law, consider how changing one variable affects the frequency and force of particle collisions with the container walls.

2. Boyle’s Law: If volume decreases, particles hit the walls more often, increasing pressure.

3. Charles’s Law: If temperature increases, particles move faster, so to keep pressure constant, volume must increase.

4. Avogadro’s Law: More particles mean more collisions, so volume must increase to keep pressure constant.

5. Dalton’s Law: Each gas acts independently, so total pressure is the sum of individual pressures.

Try explaining each law in terms of particle motion before checking the answer!

Final Answer:

• Boyle’s Law: Halving the volume doubles the pressure due to more frequent collisions.

• Charles’s Law: Doubling temperature requires doubling volume to keep pressure constant.

• Avogadro’s Law: Doubling the number of particles requires doubling the volume to keep pressure constant.

• Dalton’s Law: Each gas’s pressure is independent and additive because particles act independently.

Q5. If NH3 and HCl are each released into still air, how far will the NH3 have effused when the HCl has diffused 1.00 meter?

Background

Topic: Graham’s Law of Effusion/Diffusion

This question tests your ability to apply Graham’s Law to compare the rates of diffusion of two gases based on their molar masses.

Key Terms and Formulas:

• Graham’s Law: $\frac{\text{Rate}_1}{\text{Rate}_2} = \sqrt{\frac{M_2}{M_1}}$

• Where $M$ is the molar mass of each gas.

Step-by-Step Guidance

1. Identify the molar masses: $M_{\mathrm{NH_3}} = 17.031$ g/mol, $M_{\mathrm{HCl}} = 36.461$ g/mol.

2. Set up Graham’s Law to compare the rates (or distances) of NH3 and HCl:

   $\frac{\text{Rate}_{\mathrm{NH_3}}}{\text{Rate}_{\mathrm{HCl}}} = \sqrt{\frac{M_{\mathrm{HCl}}}{M_{\mathrm{NH_3}}}}$

3. Plug in the values for the molar masses:

   $\sqrt{\frac{36.461}{17.031}}$

4. Since HCl travels 1.00 meter, multiply this ratio by 1.00 m to find the distance NH3 travels.

Try calculating the ratio and the distance before checking the answer!

Final Answer: 1.46 meters

NH3 travels 1.46 meters when HCl travels 1.00 meter, based on the ratio of their rates from Graham’s Law.