Question

a gas is contained in a thick walled balloon. when the pressure changes from 417 mm hg to 576 mm hg, the volume changes from l to 4.78 l and the temperature changes from 497 k to 386k

Answer 1

We can use the combined gas law equation to solve for the initial volume
$\frac{P1V1}{T1} = \frac{P2V2}{T2}$
parameters for the first instance are on the left side and parameters for the second instance are on the right side of the equation 
substituting the values in the equation 
$\frac{417 mmHg*V}{497 K} = \frac{576mmHg*4.78L}{386K}$
V = 8.50 L
the initial volume is 8.50 L