To calculate the maximum work done when the pressure of 10g of hydrogen is reduced from 20atm to 10atm at a constant temperature of 273°K, we can use the formula for the work done in an isothermal process:
W = nRT ln(V2/V1)
where W is the work done, n is the number of moles of gas, R is the gas constant, T is the temperature in Kelvin, and V1 and V2 are the initial and final volumes of the gas.
First, we need to calculate the initial and final volumes of the gas using the ideal gas law:
PV = nRT
where P is the pressure, V is the volume, and n, R, and T are as defined above. Rearranging this equation to solve for V, we get:
V = (nRT)/P
Using this equation, we can calculate the initial volume of the gas:
V1 = (10 g H2 / 2.016 g/mol) * (0.0821 L·atm/mol·K) * (273 K) / (20 atm) = 11.9 L
And the final volume of the gas:
V2 = (10 g H2 / 2.016 g/mol) * (0.0821 L·atm/mol·K) * (273 K) / (10 atm) = 23.8 L
Now we can plug these values into the formula for work:
W = (10 g H2 / 2.016 g/mol) * (0.0821 L·atm/mol·K) * (273 K) * ln(23.8 L / 11.9 L) = 98.8 J
If the gas behaves ideally, there will be no change in internal energy because the temperature is constant (ΔU = 0). Therefore, the value of q in the process is equal to the negative of the work done:
q = -W = -98.8 J.