The Ideal Gas Law - AP Physics 2

1. How does the Ideal Gas Law change if $n$ is constant but $P$, $V$ change?

   Boyle's Law. Special case where $PV = $ constant at fixed amount.

2. Convert temperature from Celsius to Kelvin for gas law calculations.

   $K = °C + 273.15$. Converts to absolute scale required for gas laws.

3. Identify the units for $R$ when pressure is in Pascals.

   Joules per mole Kelvin. Energy units appropriate for Pascal pressure measurements.

4. What happens to volume if both $P$ and $T$ double, while $n$ is constant?

   Volume remains constant. Effects of pressure and temperature changes cancel out.

5. Identify the relationship between volume and temperature in the Ideal Gas Law.

   Directly proportional. Both increase or decrease together (Charles's Law).

6. Identify the relationship between pressure and volume in the Ideal Gas Law.

   Inversely proportional. When one increases, the other decreases (Boyle's Law).

7. What is the ideal gas constant $R$ value in $J/(mol \times K)$?

   $8.314 \text{ J}/(\text{mol} \times \text{K})$. Used when pressure is in Pascals and volume in cubic meters.

8. Calculate the volume if $P = 2$ atm, $n = 1$ mol, $T = 273$ K.

   $V = 11.2$ L. Using $PV = nRT$: $V = \frac{(1)(0.0821)(273)}{2} = 11.2$ L.

9. Find the pressure of 2 moles of gas at 300 K in a 10 L container.

   $P = 4.92$ atm. Using $PV = nRT$: $P = \frac{(2)(0.0821)(300)}{10} = 4.92$ atm.

10. What happens to pressure when volume decreases at constant $n$ and $T$?

    Pressure increases. Gas molecules compress into smaller space, creating higher pressure.

11. What happens to pressure when temperature decreases at constant $V$ and $n$?

    Pressure decreases. Lower kinetic energy reduces molecular collisions with walls.

12. Find the number of moles for $P = 4$ atm, $V = 15$ L, $T = 300$ K.

    $n = 2.44$ mol. Using $PV = nRT$: $n = \frac{(4)(15)}{(0.0821)(300)} = 2.44$ mol.

13. Find the temperature if $P = 3$ atm, $V = 10$ L, $n = 1$ mol.

    $T = 366$ K. Using $PV = nRT$: $T = \frac{(3)(10)}{(1)(0.0821)} = 366$ K.

14. What does the variable $n$ represent in the Ideal Gas Law?

    Number of moles of gas. Amount of substance measured in molecular units.

15. Determine $n$ for $P = 2$ atm, $V = 5$ L, $T = 298$ K.

    $n = 0.41$ mol. Using $PV = nRT$: $n = \frac{(2)(5)}{(0.0821)(298)} = 0.41$ mol.

16. What is the value of the ideal gas constant $R$ in $L \times atm/(mol \times K)$?

    $0.0821 \text{ L} \times \text{atm}/(\text{mol} \times \text{K})$. Standard value when using atm and L units.

17. What does the variable $V$ represent in the Ideal Gas Law?

    Volume of the gas. Space occupied by the gas in three dimensions.

18. Identify the units for $R$ when using $8.314$ as the constant.

    $J/(mol \times K)$. Energy per amount per temperature unit.

19. Identify the relationship between moles and volume in the Ideal Gas Law.

    Directly proportional. More gas molecules occupy more space (Avogadro's Law).

20. What is the temperature if $P = 5$ atm, $V = 20$ L, $n = 2$ mol?

    $T = 609$ K. Using $PV = nRT$: $T = \frac{(5)(20)}{(2)(0.0821)} = 609$ K.

21. State the formula for the Ideal Gas Law.

    $PV = nRT$. Relates pressure, volume, moles, and temperature for ideal gases.

22. What units must pressure be in for the Ideal Gas Law when using $R = 0.0821$?

    Atmospheres (atm). Required unit to match the gas constant $R$ value.

23. Determine $V$ for $P = 1.5$ atm, $n = 2$ mol, $T = 298$ K.

    $V = 32.6$ L. Using $PV = nRT$: $V = \frac{(2)(0.0821)(298)}{1.5} = 32.6$ L.

24. If $V$ is halved and $n$ and $T$ are constant, what happens to $P$?

    Pressure doubles. Volume is inversely proportional to pressure.

25. Calculate the temperature if $P = 1$ atm, $V = 22.4$ L, $n = 1$ mol.

    $T = 273$ K. Using $PV = nRT$: $T = \frac{(1)(22.4)}{(1)(0.0821)} = 273$ K.

26. What does the variable $P$ represent in the Ideal Gas Law?

    Pressure of the gas. Force per unit area exerted by gas molecules on container walls.

27. What happens to volume when temperature increases at constant $P$ and $n$?

    Volume increases. Higher kinetic energy causes gas to expand.

28. What does the variable $T$ represent in the Ideal Gas Law?

    Temperature in Kelvin. Absolute temperature scale starting at absolute zero.

29. If $T$ doubles and $n$ and $V$ are constant, what happens to $P$?

    Pressure doubles. Temperature is directly proportional to pressure.

30. Convert 100°C to Kelvin for use in gas law calculations.

    $373.15$ K. Add 273.15 to Celsius temperature.

31. Calculate the pressure if $n = 1$ mol, $V = 22.4$ L, $T = 273$ K.

    $P = 1$ atm. Using $PV = nRT$: $P = \frac{(1)(0.0821)(273)}{22.4} = 1$ atm.

32. Find the volume of 1 mole of gas at 1 atm and 273 K.

    $V = 22.4$ L. Standard molar volume at STP conditions.

33. What does the variable $R$ represent in the Ideal Gas Law?

    Ideal gas constant. Universal proportionality constant relating gas properties.

34. Calculate pressure when 0.5 mol of gas is at 350 K in a 5 L container.

    $P = 2.87$ atm. Using $PV = nRT$: $P = \frac{(0.5)(0.0821)(350)}{5} = 2.87$ atm.

35. In the Ideal Gas Law, what units must volume be in when using $R = 0.0821$?

    Liters (L). Volume unit that corresponds to the standard $R$ value.

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