Here are the step-by-step solutions for the four problems on your worksheet.
1. Find the new pressure ($P_2$)
*
Identify the knowns:
* $P_1 = 505 \text{ kPa}$
* $V_1 = 6.50 \text{ mL}$
* $T_1 = 300 \text{ K}$
* $P_2 = ?$ (This is what we need to find)
* $V_2 = 4.75 \text{ cm}^3$ (Note: $1 \text{ cm}^3$ is equal to $1 \text{ mL}$, so $V_2 = 4.75 \text{ mL}$)
* $T_2 = 325 \text{ K}$
*
Set up the equation:
$$\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$$
*
Rearrange to solve for $P_2$:
$$P_2 = \frac{P_1 V_1 T_2}{T_1 V_2}$$
*
Plug in the numbers:
$$P_2 = \frac{505 \times 6.50 \times 325}{300 \times 4.75}$$
$$P_2 = \frac{1,068,062.5}{1,425}$$
$$P_2 \approx 749.5 \text{ kPa}$$
***
2. Find the new volume ($V_2$)
*
Identify the knowns:
* $P_1 = 660 \text{ torr}$
* $V_1 = 36.0 \text{ mL}$
* $T_1 = 193 \text{ K}$
* $P_2 = 698 \text{ torr}$
* $V_2 = ?$
* $T_2 = 257 \text{ K}$
*
Set up the equation:
$$\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$$
*
Rearrange to solve for $V_2$:
$$V_2 = \frac{P_1 V_1 T_2}{T_1 P_2}$$
*
Plug in the numbers:
$$V_2 = \frac{660 \times 36.0 \times 257}{193 \times 698}$$
$$V_2 = \frac{6,126,480}{134,714}$$
$$V_2 \approx 45.5 \text{ mL}$$
***
3. Find the new volume ($V_2$) with temperature conversion
*
Important Step: Convert Celsius to Kelvin first!
* $T_1 = 27^\circ\text{C} + 273 = 300 \text{ K}$
* $T_2 = -12^\circ\text{C} + 273 = 261 \text{ K}$
*
Identify the knowns:
* $P_1 = 1.65 \text{ atm}$
* $V_1 = 343 \text{ mL}$
* $T_1 = 300 \text{ K}$
* $P_2 = 2.10 \text{ atm}$
* $V_2 = ?$
* $T_2 = 261 \text{ K}$
*
Set up the equation:
$$\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$$
*
Rearrange to solve for $V_2$:
$$V_2 = \frac{P_1 V_1 T_2}{T_1 P_2}$$
*
Plug in the numbers:
$$V_2 = \frac{1.65 \times 343 \times 261}{300 \times 2.10}$$
$$V_2 = \frac{147,598.95}{630}$$
$$V_2 \approx 234 \text{ mL}$$
***
4. Find the new temperature ($T_2$)
*
Identify the knowns:
* $P_1 = 325 \text{ kPa}$
* $V_1 = 3.25 \text{ L}$
* $T_1 = 298 \text{ K}$
* $P_2 = 218 \text{ kPa}$
* $V_2 = 4.50 \text{ L}$
* $T_2 = ?$
*
Set up the equation:
$$\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$$
*
Rearrange to solve for $T_2$:
$$T_2 = \frac{P_2 V_2 T_1}{P_1 V_1}$$
*
Plug in the numbers:
$$T_2 = \frac{218 \times 4.50 \times 298}{325 \times 3.25}$$
$$T_2 = \frac{292,122}{1,056.25}$$
$$T_2 \approx 277 \text{ K}$$
Final Answer:
1. 749.5 kPa
2. 45.5 mL
3. 234 mL
4. 277 K
Parent Tip: Review the logic above to help your child master the concept of combined gas law worksheet.
