Problem 115 A flask containing 2.0 moles of He gas at ( 1.0 mathrm{~atm} ) and ( 300 mathrm{~K} ) is connected to another flask containing ( mathrm{N}_{2}(g) ) at the same temperature and pressure by a narrow tube of negligible volume. Volume of the nitrogen flask is three times volume of He-flask. Now the He-flask is placed in a thermostat at ( 200 mathrm{~K}_{text {and }} mathrm{N}_{2} )-flask in another thermostat at ( 400 mathrm{~K} ). Determine final pressure and final number of moles in each flask.

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Step:1 ：1. Use ideal gas law to find volume of He flask: ( V_{He} = frac{n_{He}RT}{P} )Step:2 ：2. Calculate volume of N2 flask: ( V_{N2} = 3 * V_{He} )Step:3 ：3. Determine total volume after temperature change: ( V_{He}^{&#x27;} = frac{n_{He}R(200)}{1.0} )Step:4 ：( V_{N2}^{&#x27;} = frac{3n_{He}R(400)}{1.0} )Step:5 ：4. Calculate final pressure: ( P_{final} = frac{n_{He}RT_{1}+3n_{He}RT_{2}}{V_{He}^{&#x27;}+V_{N2}^{&#x27;}} )Step:6 ：5. Update the number of moles: ( n_{He}^{&#x27;} = frac{2}{1+n} )Step:7 ：( n_{N2}^{&#x27;} = frac{2n}{1+n} )Step:8 ：6. Solve for n: ( n = frac{3(400)-200}{300} - 1 )

Answer

Step: 1 ：1. Use ideal gas law to find volume of He flask: ( V_{He} = frac{n_{He}RT}{P} )Step: 2 ：2. Calculate volume of N2 flask: ( V_{N2} = 3 * V_{He} )Step: 3 ：3. Determine total volume after temperature change: ( V_{He}^{&#x27;} = frac{n_{He}R(200)}{1.0} )Step: 4 ：( V_{N2}^{&#x27;} = frac{3n_{He}R(400)}{1.0} )Step: 5 ：4. Calculate final pressure: ( P_{final} = frac{n_{He}RT_{1}+3n_{He}RT_{2}}{V_{He}^{&#x27;}+V_{N2}^{&#x27;}} )Step: 6 ：5. Update the number of moles: ( n_{He}^{&#x27;} = frac{2}{1+n} )Step: 7 ：( n_{N2}^{&#x27;} = frac{2n}{1+n} )Step: 8 ：6. Solve for n: ( n = frac{3(400)-200}{300} - 1 )

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