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Chapter 3: Q15E (page 610)

A metal tank with volume 3.10 L will burst if the absolute pressure of the gas it contains exceeds 100 atm. (a) If 11.0 mol of an ideal gas is put into the tank at 23.0°C, to what temperature can the gas be warmed before the tank ruptures? Ignore the thermal expansion of the tank. (b) Based on your answer to part (a), is it reasonable to ignore the thermal expansion of the tank? Explain.

Short Answer

Expert verified

  1. 343.3K of temperature that can warm the gas.

  2. Thermal expansion in the tank is negligible as the increase in temperature is not high.

Step by step solution

01

Step: 1

Given data:

VolumeV1=3.1L, Pressure P2=100atm, Temperature T1=296K,n=11mol

Initial pressure from Ideal Gas Equation

PV=nRTP=nRTV=11×8.3145×2963.1×10-3P=8.737×106Pa

02

Step: 2

Comparing two-state for warm temperatureT2

P1V1T1=P2V2T2V1=V2T2=P2×T1P1=100×1.013×105×2968.737×106=343.4K

343.3K of temperature that can warm the gas

03

Step: 3

Change in temperature

∆T=343.4-296=47K

Thermal expansion in the tank is negligible as the increase in temperature is not high.

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