Liquid water can be separated into hydrogen gas and oxygen gas through electrolysis. 1 mole of hydrogen gas and 0.5 moles of oxygen gas is produced 1 mole of liquid water collected in separate 10L containers at 1 atm. Will the temperatures of the gases be equal? Use the ideal gas law.

Answer 1

To determine whether the temperatures of the gases will be equal, we can use the ideal gas law equation: PV = nRT.

Given that 1 mole of hydrogen gas is produced in a 10L container at 1 atm, we can calculate the hydrogen gas's temperature:

PV = nRT
(1 atm)(10L) = (1 mole)(R)(T)

Rearranging the equation to solve for T, we get:

T = (PV) / (nR)

Plugging in the values:

T = (1 atm)(10L) / (1 mole)(R)

Now, given that 0.5 moles of oxygen gas are produced in another separate 10L container at 1 atm, we can calculate the oxygen gas's temperature using the same equation:

T = (PV) / (nR)
T = (1 atm)(10L) / (0.5 moles)(R)

Since R is a constant, we can see that both the hydrogen gas and oxygen gas will have the same temperature, as T is directly proportional to PV and inversely proportional to n.

Therefore, the temperatures of the gases will be equal.