To calculate the number of moles of a gas that occupy 647.8 mL at 5.329 x 10^-1 atm and 35.00 °C, we can use the ideal gas law formula PV = nRT where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant and T is the temperature in Kelvin.
Firstly, we need to convert the temperature from Celsius to Kelvin by adding 273.15 to it. So T = 35.00 + 273.15 = 308.15 K.
The ideal gas constant R is equal to 0.08206 L atm mol^-1 K^-1.
Substituting these values into the ideal gas law formula gives:
n = PV/RT = (5.329 x 10^-1 atm) x (647.8 mL / 1000 mL/L) / (0.08206 L atm mol^-1 K^-1 x 308.15 K) = 0.0136 moles.
Therefore, there are approximately 0.0136 moles of gas that occupy 647.8 mL at 5.329 x 10^-1 atm and 35.00 °C.