A gas has a density of $3.18 \cdot g \cdot L^{- 1}$ $3.18gL^-1$ at a temperature of $347 \cdot K$ $347K$ , and a pressure of $1.2 \cdot a t m$ $1.2atm$ . What is its molecular mass?

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A gas has a density of $3.18 \cdot g \cdot L^{- 1}$ $3.18gL^-1$ at a temperature of $347 \cdot K$ $347K$ , and a pressure of $1.2 \cdot a t m$ $1.2atm$ . What is its molecular mass?

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Answer 1 · 2017-04-03T05:40:26

We use the Ideal Gas equation to get $molecular mass = 75.5 \cdot g \cdot m o l^{- 1}$ $"molecular mass"=75.5*g*mol^-1$

Explanation:

We assume ideality, and so $P V = n R T$ $PV=nRT$ , and thus,

$P V = (\frac{mass}{molar mass}) R T$ $PV=("mass"/"molar mass")RT$ because $n = \frac{mass}{molar mass}$ $n="mass"/"molar mass"$

On rearrangement, $molar mass = \frac{mass}{V} \times \frac{R T}{P}$ $"molar mass"="mass"/Vxx(RT)/P$

But $\frac{mass}{V} = ρ, density$ $"mass"/V=rho, "density"$ , and thus...........

$molar mass = \frac{ρ R T}{P} =$ $"molar mass"=(rhoRT)/P=$

$\frac{3.18 \cdot g \cdot L^{- 1} \times 0.0821 \cdot \frac{L \cdot a t m}{K \cdot m o l} \times 347 \cdot K}{1.2 \cdot a t m}$ $(3.18*g*L^-1xx0.0821*(L*atm)/(K*mol)xx347*K)/(1.2*atm)$

Let's just cancel out the units to see if we have got this right. I am not immune to mistakes.............

$"Molar mass"=(3.18*g*cancel(L^-1)xx0.0821*cancel(L*atm)/(cancelK*mol)xx347*cancelK)/(1.2*cancel"atm")$

And this gives, I think, an answer of........

$75.5*g*mol^-1$ . Because we have got consistent units, I think our order of operations is correct.

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A gas has a density of $3.18 \cdot g \cdot L^{- 1}$ $3.18gL^-1$ at a temperature of $347 \cdot K$ $347K$ , and a pressure of $1.2 \cdot a t m$ $1.2atm$ . What is its molecular mass?

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Explanation:

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A gas has a density of 3.18*g*L^-13.18⋅g⋅L−13.18*g*L^-1 at a temperature of 347*K347⋅K347*K, and a pressure of 1.2*atm1.2⋅atm1.2*atm. What is its molecular mass?

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A gas has a density of $3.18 \cdot g \cdot L^{- 1}$ $3.18gL^-1$ at a temperature of $347 \cdot K$ $347K$ , and a pressure of $1.2 \cdot a t m$ $1.2atm$ . What is its molecular mass?