[benworld]

1. The problem statement
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A Sample of gas 250 mL at 37 C and 730 torr . What volume would gas occupy at standard conditions ?

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2. Relevant equations
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pv = nRT

V2 = T2P1V1
-------
T1P2

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3. The attempt at a solution
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Sample Gas

V = 250 mL ( 0.250 L )
P = 730 torr ( .960 atm )
T = 310 K

Standard Condition

T = 273
V = 22.4 L
P = 1 atm

I'm confused because sample gas formula is already given and then find the gas under stand condition ?

Do I just use standard condition formula and drop the other ones ?


If I use pv = nRT then I get following

v = (0.250 L / 22.4 L = .0111 mol) since STP 1 mol = 22.4 L
p = .960 atm
R = 0.08260 ( constant gas )
T = 310 K

v = (.0111 mol ) (0.08260)(310)
--------------------------
.960 atm

Answer = .290 L

The answer doesn't seem to make sense. Any correction ?

[Borek]

Try P₁V₁/T₁ = P₂V₂/T₂ - you know P₁, V₁ & T₁ and you are given P₂ & T₂.

[benworld]

got it ..thanks. .. 211 ML

[billnotgatez]

What the original posting missed was that the number of moles in the sample situation was not one mole. So when using that same amount of gas at STP, they could not have 22.4 L volume.

When analyzing the problem in general it looks like you can look at it as an ideal gas in situation 1 and situation 2.

Mathematically it can be represented by
Situation 1 ---- P₁ V₁= n₁ R T₁
Situation 2 ---- P₂ V₂= n₂ R T₂

It follows mathematically

Situation 1 ---- R = (P₁ V₁) / (n₁ T₁)
Situation 2 ---- R = (P₂ V₂) / (n₂ T₂)

Since R is the same in both situations

(P₁ V₁) / (n₁ T₁)= (P₂ V₂) / (n₂ T₂)

For this problem

Although the the n (number of moles) is not one, it is the same for both situations and can be canceled out of the equation.

(P₁ V₁) / T₁)= (P₂ V₂) / T₂)

You then solve for V₂ making sure all the units are the same and the values are absolute.