Question

An empty cylindrical canister 1.50 m long and 90.0 cm in diameter is to be filled with pure oxygen at 22.0C22.0^{\circ} \mathrm{C} to store in a space station. To hold as much gas as possible, the absolute pressure of the oxygen will be 21.0 atm. The molar mass of oxygen is 32.0 g/mol. (a) How many moles of oxygen does this canister hold? (b) For someone lifting this canister, by how many kilograms does this gas increase the mass to be lifted?

Solution

Verified
Answered 3 months ago
Answered 3 months ago
Step 1
1 of 2

Given

T=295K,L=1.5m,P=21atm,M=32g/mol,r=0.45mT = 295 \,\,\mathrm{K} ,\, L =1.5 \,\,\mathrm{m},\, P= 21 \,\,\mathrm{atm},\, M = 32 \,\,\mathrm{g/mol},\, r = 0.45 \,\,\mathrm{m}

Solution

a)
first we need to calculate the volume VV of the cylinder to know the volume of Oxygen

V=πr2L=π×(0.45m)2×1.5m=0.953m3\begin{aligned} V &= \pi \cdot r^{2} \cdot L\\ &= \pi \times (0.45 \,\,\mathrm{m})^{2} \times 1.5 \,\,\mathrm{m}\\ &= 0.953 \,\,\mathrm{m^{3}} \end{aligned}

Now to calculate the number of moles nn that the cylinder can hold we would apply the Ideal Gas equation

pV=nRTp\cdot V = n\cdot R\cdot T

by solving for nn

n=PVRT=21atm×1.013×105Pa/atm×0.953m38.315J/molK×295K=827mol\begin{aligned} n& = \dfrac{P\cdot V}{R\cdot T}\\ & = \dfrac{21 \,\,\mathrm{atm} \times 1.013 \times 10^{5} \,\,\mathrm{Pa/atm} \times 0.953 \,\,\mathrm{m^{3}}}{8.315 \,\,\mathrm{J/mol\cdot K} \times 295 \,\,\mathrm{K}} \\ &= \boxed{827 \,\,\mathrm{mol}} \end{aligned}

Note
We sub with the pressure in Pa unit so the pressure multiplied by 1.013×105Pa/atm1.013 \times 10^{5} \,\,\mathrm{Pa/atm}

Create an account to view solutions

By signing up, you accept Quizlet's Terms of Service and Privacy Policy
Continue with GoogleContinue with Facebook

Create an account to view solutions

By signing up, you accept Quizlet's Terms of Service and Privacy Policy
Continue with GoogleContinue with Facebook

Recommended textbook solutions

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics 4th Edition by Randall D. Knight

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

4th EditionISBN: 9780133942651 (5 more)Randall D. Knight
3,508 solutions
Sears and Zemansky's University Physics 14th Edition by Hugh D. Young, Roger A. Freedman

Sears and Zemansky's University Physics

14th EditionISBN: 9780133969290 (1 more)Hugh D. Young, Roger A. Freedman
8,341 solutions
Mathematical Methods in the Physical Sciences 3rd Edition by Mary L. Boas

Mathematical Methods in the Physical Sciences

3rd EditionISBN: 9780471198260Mary L. Boas
3,355 solutions
Fundamentals of Physics 10th Edition by David Halliday, Jearl Walker, Robert Resnick

Fundamentals of Physics

10th EditionISBN: 9781118230718David Halliday, Jearl Walker, Robert Resnick
8,950 solutions

More related questions

1/2

1/3