This can be solved using the Combined Gas Law. The formula for that is
[tex]\frac{P_{1} V_{1} }{T_{1} } = \frac{P_{2} V_{2} }{T_{2} }[/tex]
Let's go ahead and fill in our known values. Since pressure remains the same, it doesn't matter what number we use, so let's assume 1 atm on both sides. For temperature, remember to convert it to Kelvin first (K = C + 273).
[tex]\frac{(1 atm) (0.400 L)}{(323 K)} = \frac{(1 atm) (x L)}{(573 K)}[/tex]
Go ahead and simplify both sides.
0.001238 = [tex]\frac{(x L)}{(573 K)}[/tex]
Multiply both sides by 573.
0.7095 = x L
So, at 300° C, your gas will occupy 0.7095 L.
