Hydrogen gas (H2) is generated by the following reaction.
Ca(s) + 2 HCl(aq) → CaCl2(aq) + H2(g);
ΔH = −542.7 kJ/mol
When this reaction takes place in a cylinder (fitted with a piston) containing 1.000 mol Ca(s), 542.7 kJ heat is lost to the surroundings. Because a gas is generated, work is done by the system against a constant pressure of 1.140 atm. If the internal energy decreases by 545.53 kJ,
what is the change in the volume of the system in liters?
dE = q + w
Substitute dE and q and solve for w (in joules).
Convert to L*atm knowing that 1 L*atm = 101.325 J.
Then w = -pdV and solve for dV.
To find the change in volume of the system, we need to consider the work done by the system against a constant pressure. The equation for work done is given by:
Work = -P * ΔV
Where P is the pressure and ΔV is the change in volume.
In this case, the pressure is given as 1.140 atm and the work done is equal to the heat lost to the surroundings, which is 542.7 kJ. We also know that the internal energy decreased by 545.53 kJ.
Since the work done is equal to the heat lost to the surroundings, we can write:
Work = -542.7 kJ
Now, we can rearrange the equation to solve for the change in volume:
-542.7 kJ = -P * ΔV
Substituting the given pressure:
-542.7 kJ = -1.140 atm * ΔV
To calculate the change in volume, we need to convert the pressure from atm to kJ/L. Since 1 atm is equivalent to 101.325 kJ/L, we have:
-542.7 kJ = -1.140 * 101.325 kJ/L * ΔV
Now, we can solve for ΔV:
ΔV = -542.7 kJ / (-1.140 * 101.325 kJ/L)
ΔV ≈ 4.85 L
Therefore, the change in volume of the system is approximately 4.85 liters.