Question:
Calculate the temperature of 2 moles of gas occupying a volume of 5.0 liters at 24.6 atmospheres?
(\(R = 0.0821\) L atm K\(^{-1}\) mol\(^{-1}\))
Calculate the temperature of 2 moles of gas occupying a volume of 5.0 liters at 24.6 atmospheres?
(\(R = 0.0821\) L atm K\(^{-1}\) mol\(^{-1}\))
(\(R = 0.0821\) L atm K\(^{-1}\) mol\(^{-1}\))
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Use \(PV=nRT\) and convert the Kelvin result to Celsius.
Updated On: Oct 1, 2026
- \(476^{\circ}\)C
- \(480^{\circ}\)C
- \(440^{\circ}\)C
- \(450^{\circ}\)C
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The Correct Option is A
Solution and Explanation
Step 1: Key Formula:
The ideal gas equation is \(PV = nRT\), so \(T = \frac{PV}{nR}\).
Step 2: Calculate:
\[ T = \frac{24.6\times5.0}{2\times0.0821} = \frac{123}{0.1642} = 749.1\ \text{K} \]
Convert to Celsius: \(749.1 - 273 = 476.1^{\circ}\text{C}\), about \(476^{\circ}\)C.
Step 3: Other options:
Values \(440\), \(450\) and \(480^{\circ}\)C do not match \(T = 749\) K, and \(749\) K itself is not listed, since the options are in Celsius.
Final Answer:
The temperature is about \(476^{\circ}\)C, option (A). \[ \boxed{476^{\circ}\text{C}} \]
The ideal gas equation is \(PV = nRT\), so \(T = \frac{PV}{nR}\).
Step 2: Calculate:
\[ T = \frac{24.6\times5.0}{2\times0.0821} = \frac{123}{0.1642} = 749.1\ \text{K} \]
Convert to Celsius: \(749.1 - 273 = 476.1^{\circ}\text{C}\), about \(476^{\circ}\)C.
Step 3: Other options:
Values \(440\), \(450\) and \(480^{\circ}\)C do not match \(T = 749\) K, and \(749\) K itself is not listed, since the options are in Celsius.
Final Answer:
The temperature is about \(476^{\circ}\)C, option (A). \[ \boxed{476^{\circ}\text{C}} \]
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