If a gas occupies a container of volume 146 cm3 at 18°C and 0.971 atm, its volume in cm3 at s.t.p is?

 If a gas occupies a container of volume 146 cm3 at 18°C and 0.971 atm, its volume in cm3 at s.t.p is?

• A. 133
• B. 146
• C. 266
• D. 292

Answer is A

Solution

We’re solving this using the Combined Gas Law:

$$\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$$

Where:

• $P_1 = 0.971 \, \text{atm}$

• $V_1 = 146 \, \text{cm}^3$

• $T_1 = 18^\circ C = 18 + 273 = 291 \, K$

• At S.T.P.: $P_2 = 1 \, \text{atm}, T_2 = 273 \, K$

• $V_2 = ?$

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Step 1: Rearrange

$$V_2 = \frac{P_1 V_1 T_2}{P_2 T_1}$$

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Step 2: Substitute values

$$V_2 = \frac{0.971 \times 146 \times 273}{1 \times 291}$$

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Step 3: Multiply numerator

• $0.971 \times 146 = 141.866$

• $141.866 \times 273 = 38,726.3$

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Step 4: Divide by denominator

$$V_2 = \frac{38,726.3}{291} \approx 133.1$$

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Jamb 1990 question 5