Question

The volume of a sample of gas measured at 35.0°C and 1.00 atm pressure is 3.00 L. What must the final temperature be in order for the gas to have a final volume of 4.00 L at 1.00 atm pressure? ALL CALCULATIONS MUST BE PROVIDED FOR FULL CREDIT - 42.0°C -226.3°C 137.7°C 46.7°C 26.3°C

Answer 1

As per ideal gas law :
PV = nRT
where, P is the pressure of gas, V is the volume, n is the number of moles of gas, R is the universal gas constan and T is the absolute temperature in kelvins. [Note that, this equation must be true for temperatures till absolute 0 K , and it can not be true if T is taken in degree celsius]

Given:
At P = 1atm and T = 35'C = 35 + 273.15 K =308.15K -> V= 3.00 L [Case1]
Finally we have to achieve:
V = 4.00L at P = 1atm. [Case2]
we need to find temperature for the final condition.

From the ideal gas law we can write:
$\frac{PV}{T} = nR$
For a gas with constant number of moles, this value of PV/T remains constant.

So, for both cases:
$\frac{P_{1}V_{1}}{T_{1}} = \frac{P_{2}V_{2}}{T_{2}}$
P₁ = 1atm V₁= 3.00 L T₁ = 308.15K
P₂ = 1atm V₂= 4.00 L T₂ = ?

Putting all these values:

1 x 3.00 1 x 4.00 T, 308.15

$T_{2} = \frac{4 \times 308.15K}{3} = \frac{1232.6K}{3} = 410.86K$

T₂ = 410.86 - 273.15 'C = 137.71'C

Correct answer- option 3: 137.7'C