Gas Laws and Kinetic Molecular Theory (4B) - Chem & Physics

1. What is the Kelvin temperature conversion formula from Celsius $\left(^\circ\text{C}\right)$?

   $T(\text{K}) = T(^\circ\text{C}) + 273.15$. Absolute temperature in Kelvin is obtained by adding 273.15 to the Celsius temperature to align with the ideal gas law scale.

2. What is the value of $R$ in $\text{J}\cdot\text{mol}^{-1}\cdot\text{K}^{-1}$?

   $R = 8.314\ \text{J}\cdot\text{mol}^{-1}\cdot\text{K}^{-1}$. This value of $R$ is employed in the ideal gas law when energy units (joules) are required.

3. Find $n$ if $P = 2\ \text{atm}$, $V = 5\ \text{L}$, $T = 300\ \text{K}$, and $R = 0.082\ \text{L atm mol}^{-1}\text{K}^{-1}$.

   $n \approx 0.41\ \text{mol}$. Solving the ideal gas law for $n$ gives moles as pressure times volume over $R$ times temperature.

4. What molar volume does an ideal gas occupy at STP (approximate MCAT value)?

   $22.4\ \text{L mol}^{-1}$. At STP, one mole of ideal gas occupies this volume, derived from the ideal gas law with $P=1$ atm and $T=273$ K.

5. State the formula for Boyle's law relating pressure and volume at constant $T$ and $n$.

   $P_1V_1 = P_2V_2$. Boyle's law describes the inverse relationship between pressure and volume for a fixed amount of gas at constant temperature.

6. State the mole fraction definition for component $i$ in a gas mixture.

   $x_i = \frac{n_i}{n_{\text{total}}}$. Mole fraction represents the ratio of moles of one component to total moles in the mixture.

7. Find $P_2$ if $P_1 = 1.5\ \text{atm}$, $T_1 = 300\ \text{K}$, and $T_2 = 200\ \text{K}$ at constant $V$.

   $P_2 = 1.0\ \text{atm}$. By Gay-Lussac's law, pressure decreases with the ratio of temperatures at constant volume.

8. Identify the key ideal-gas assumptions about particle volume and intermolecular forces.

   Negligible particle volume; no intermolecular attractions or repulsions. Ideal gas assumptions simplify behavior by treating particles as point masses with no volume and no interactions except elastic collisions.

9. Find $V_2$ if $V_1 = 4\ \text{L}$, $T_1 = 300\ \text{K}$, and $T_2 = 450\ \text{K}$ at constant $P$.

   $V_2 = 6\ \text{L}$. Using Charles's law, volume increases proportionally with the ratio of temperatures at constant pressure.

10. State the molar-average kinetic energy relation to temperature using $R$.

    $\langle KE \rangle_{\text{mol}} = \frac{3}{2}RT$. For one mole, average kinetic energy relates to temperature via the gas constant $R$, derived from per-molecule kinetic energy.

11. State the formula for Charles's law relating volume and temperature at constant $P$ and $n$.

    $\frac{V_1}{T_1} = \frac{V_2}{T_2}$. Charles's law indicates that volume is directly proportional to absolute temperature for a gas at constant pressure and moles.

12. State the relationship between partial pressure and mole fraction for an ideal gas mixture.

    $P_i = x_i P_{\text{total}}$. Partial pressure of a gas in a mixture is its mole fraction times the total pressure, assuming ideal behavior.

13. State Dalton's law formula for total pressure of a gas mixture.

    $P_{\text{total}} = \sum_i P_i$. Dalton's law states that in a mixture of non-reacting gases, total pressure equals the sum of each gas's partial pressure.

14. State the formula for Avogadro's law relating volume and moles at constant $P$ and $T$.

    $\frac{V_1}{n_1} = \frac{V_2}{n_2}$. Avogadro's law states that volume is directly proportional to the number of moles for a gas at constant pressure and temperature.

15. What is the standard temperature and pressure (STP) definition used on the MCAT?

    $T = 273.15\ \text{K},\ P = 1\ \text{atm}$. STP conditions provide a reference point for gas properties, with temperature at freezing point of water in Kelvin and pressure at sea level.

16. State Graham's law for the ratio of diffusion (or effusion) rates of two gases.

    $\frac{r_1}{r_2} = \sqrt{\frac{M_2}{M_1}}$. Graham's law indicates that diffusion or effusion rates are inversely proportional to the square root of molar masses.

17. State the kinetic molecular theory relation between average kinetic energy and temperature.

    $\langle KE \rangle = \frac{3}{2}k_BT$. Kinetic molecular theory posits that average kinetic energy per molecule is directly proportional to absolute temperature, with $k_B$ as Boltzmann's constant.

18. What is the value of the ideal gas constant $R$ in $\text{L}\cdot\text{atm}\cdot\text{mol}^{-1}\cdot\text{K}^{-1}$?

    $R = 0.08206\ \text{L}\cdot\text{atm}\cdot\text{mol}^{-1}\cdot\text{K}^{-1}$. This value of $R$ is used when pressure is in atm, volume in L, and temperature in K for the ideal gas law.

19. Find $V_2$ if $P_1 = 2\ \text{atm}$, $V_1 = 3\ \text{L}$, and $P_2 = 1\ \text{atm}$ at constant $T$.

    $V_2 = 6\ \text{L}$. Applying Boyle's law, volume doubles when pressure halves at constant temperature.

20. State the formula for Gay-Lussac's law relating pressure and temperature at constant $V$ and $n$.

    $\frac{P_1}{T_1} = \frac{P_2}{T_2}$. Gay-Lussac's law shows that pressure is directly proportional to absolute temperature for a gas at constant volume and moles.

21. State the ideal gas law equation relating $P$, $V$, $n$, $R$, and $T$.

    $PV = nRT$. The ideal gas law combines relationships among pressure, volume, moles, and temperature for an ideal gas using the gas constant $R$.

22. Identify the condition when real gases deviate most from ideal behavior (in terms of $P$ and $T$).

    High $P$ and low $T$. Real gases deviate from ideality when intermolecular forces and particle volume become significant under high pressure and low temperature.

23. State the combined gas law relating $P$, $V$, and $T$ for a fixed amount of gas.

    $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$. The combined gas law integrates Boyle's, Charles's, and Gay-Lussac's laws for a constant amount of gas.

24. Find $P_{\text{He}}$ if $x_{\text{He}} = 0.25$ and $P_{\text{total}} = 4\ \text{atm}$ for an ideal mixture.

    $P_{\text{He}} = 1\ \text{atm}$. Partial pressure equals mole fraction times total pressure in an ideal gas mixture per Dalton's law.

25. State the root-mean-square speed formula $u_{\text{rms}}$ for an ideal gas.

    $u_{\text{rms}} = \sqrt{\frac{3RT}{M}}$. Root-mean-square speed measures the square root of the average of squared speeds, depending on temperature and molar mass $M$.

Study these flashcards