Question:
A gas undergoes a process in which state variable changes from (1 atm, 60 mL, 27°C) to (P atm, 30 mL, 77°C). Then, \( P \) is
A gas undergoes a process in which state variable changes from (1 atm, 60 mL, 27°C) to (P atm, 30 mL, 77°C). Then, \( P \) is
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Use the combined gas law to solve for unknown variables when pressure, volume, and temperature change.
Updated On: Jan 29, 2026
- 3 atm
- \( \frac{5}{4} \) atm
- \( \frac{7}{3} \) atm
- \( \frac{4}{3} \) atm
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The Correct Option is C
Solution and Explanation
Step 1: Apply the combined gas law.
The combined gas law is given by: \[ \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}. \] Substitute the given values for the initial and final states: \[ \frac{1 \, \text{atm} \times 60 \, \text{mL}}{27°C + 273} = \frac{P \times 30 \, \text{mL}}{77°C + 273}. \] \[ \frac{1 \times 60}{300} = \frac{P \times 30}{350}. \] Step 2: Solve for \( P \).
Cross-multiply to find \( P \): \[ P = \frac{60 \times 350}{300 \times 30} = \frac{7}{3} \, \text{atm}. \] Final Answer: \[ \boxed{\frac{7}{3} \, \text{atm}}. \]
The combined gas law is given by: \[ \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}. \] Substitute the given values for the initial and final states: \[ \frac{1 \, \text{atm} \times 60 \, \text{mL}}{27°C + 273} = \frac{P \times 30 \, \text{mL}}{77°C + 273}. \] \[ \frac{1 \times 60}{300} = \frac{P \times 30}{350}. \] Step 2: Solve for \( P \).
Cross-multiply to find \( P \): \[ P = \frac{60 \times 350}{300 \times 30} = \frac{7}{3} \, \text{atm}. \] Final Answer: \[ \boxed{\frac{7}{3} \, \text{atm}}. \]
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