Question

An empty cylindrical canister 1.50 m long and 90.0 cm in diameter is to be filled with pure oxygen at $22.0^{\circ} \mathrm{C}$ 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

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Given

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

Solution

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

\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 $n$ that the cylinder can hold we would apply the Ideal Gas equation

$p\cdot V = n\cdot R\cdot T$

by solving for $n$

\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 $1.013 \times 10^{5} \,\,\mathrm{Pa/atm}$

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