Question

Here's a precise problem for a chemistry student to solve:A gas, initially at a pressure of 1 atm and a temperature of 20°C, is contained in a cylinder with a volume of 5 L. If the gas is allowed to expand to a volume of 10 L at a constant temperature of 20°C, what is the final pressure of the gas? Use the ideal gas law equation to solve the problem.

Answer 1

To solve this problem, we will use the ideal gas law equation, which is:PV = nRTwhere P is the pressure, V is the volume, n is the number of moles of the gas, R is the ideal gas constant, and T is the temperature in Kelvin.First, we need to convert the initial temperature from Celsius to Kelvin:T_initial = 20C + 273.15 = 293.15 KSince the temperature remains constant throughout the process, T_final = T_initial = 293.15 K.Now, we can use the ideal gas law equation to find the number of moles of the gas  n  initially:P_initial * V_initial = n * R * T_initial1 atm * 5 L = n * 0.0821 L atm/mol K * 293.15 Kn =  1 atm * 5 L  /  0.0821 L atm/mol K * 293.15 K  = 0.204 mol  approximately Now that we have the number of moles of the gas, we can find the final pressure  P_final  after the gas has expanded to a volume of 10 L:P_final * V_final = n * R * T_finalP_final * 10 L = 0.204 mol * 0.0821 L atm/mol K * 293.15 KP_final =  0.204 mol * 0.0821 L atm/mol K * 293.15 K  / 10 L = 0.5 atmSo, the final pressure of the gas after expanding to a volume of 10 L at a constant temperature of 20C is 0.5 atm.