The change in volume, calculated using the ideal gas law, is approximately 0.322 L, indicating a 55.84% increase from the initial volume.
To calculate the change in volume, we can use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin. Since the pressure and temperature change, we can set up the equation using the initial and final conditions:
(568 torr)(V_1) = (0.35 mol)(0.0821 L·atm/mol·K)(286 K)
(897 torr)(V_2) = (0.35 mol)(0.0821 L·atm/mol·K)(329 K)
By dividing the second equation by the first and rearranging, we can solve for V2/V1, which represents the change in volume:
V_2/V_1 = [(897 torr)(0.0821 L·atm/mol·K)(329 K)] / [(568 torr)(0.0821 L·atm/mol·K)(286 K)]
Simplifying the equation gives us V_2/V_1 = 1.5584, which means that the volume increases by approximately 1.5584 times or 55.84%. To find the actual change in volume, we multiply this value by the initial volume:
Change in Volume = V_2 - V_1
= (V_2/V_1)(V_1) - V_1
Change in Volume = (1.5584)(0.35 mol)(0.0821 L·atm/mol·K)(286 K) - (0.35 mol)(0.0821 L·atm/mol·K)(286 K)
Simplifying the equation gives us a change in volume of approximately 0.322 L.