Using data from the following reactions and applying Hess's law, calculate the heat change for the slow reaction of zinc with water (answer must be in kJ/mol Zn):
Zn(s) + 2 H2O(l) ----> Zn^2+(aq) + 2 OH-(aq) + H2(g) (ΔHrxn = ?)
H+(aq) + OH-(aq) ----> H2O(l) (ΔHrxn,1 = -56 kJ/mol H2O)
Zn(s) ----> Zn^2+(aq) (ΔHrxn,2 = -153.9 kJ)
1/2 H2(g) ----> H+(aq) (ΔHrxn,3 = 0.0 kJ)
990
To calculate the heat change for the slow reaction of zinc with water, we can use Hess's law, which states that the total enthalpy change for a reaction is independent of the pathway taken to get from reactants to products.
Hess's law allows us to manipulate the given reactions in order to obtain the desired reaction. We can use the given reactions to build the slow reaction of zinc with water.
Given reactions:
1) Zn(s) ----> Zn^2+(aq) (ΔHrxn,2 = -153.9 kJ)
2) 1/2 H2(g) ----> H+(aq) (ΔHrxn,3 = 0.0 kJ)
3) H+(aq) + OH-(aq) ----> H2O(l) (ΔHrxn,1 = -56 kJ/mol H2O)
Now, let's manipulate the given reactions to obtain the slow reaction.
First, we need to cancel out the common species, Zn^2+(aq). This can be achieved by doubling equation 1) and adding it to equation 3):
2 * Zn(s) ----> 2 * Zn^2+(aq) + 2 * OH-(aq) (ΔHrxn = -2 * 153.9 kJ)
H+(aq) + OH-(aq) ----> H2O(l) (ΔHrxn,1 = -56 kJ/mol H2O)
Next, we need to cancel out OH-(aq). We can achieve this by doubling equation 3) and adding it to equation 2):
2 * H+(aq) + 2 * OH-(aq) ----> 2 * H2O(l) (ΔHrxn = -2 * 56 kJ/mol H2O)
1/2 H2(g) ----> H+(aq) (ΔHrxn,3 = 0.0 kJ)
Now, we have canceled out the common species Zn^2+(aq) and OH-(aq). We can add these two manipulated reactions to obtain the slow reaction:
2 * Zn(s) + 1/2 H2(g) ----> 2 * Zn^2+(aq) + 2 * OH-(aq) + H2(g) (ΔHrxn = -2 * 153.9 kJ + 0.0 kJ - 2 * 56 kJ/mol H2O)
Now, we can calculate the heat change for the slow reaction:
ΔHrxn = -2 * 153.9 kJ + 0.0 kJ - 2 * 56 kJ/mol H2O
Calculating the values:
ΔHrxn = -307.8 kJ - 112 kJ/mol H2O
Therefore, the heat change for the slow reaction of zinc with water is -307.8 kJ - 112 kJ/mol H2O.
To get the answer in kJ/mol Zn, you can divide the heat change by the molar ratio between Zn and H2 in the balanced equation. The balanced equation shows that for every 2 moles of Zn, we have 1 mole of H2:
ΔHrxn = (-307.8 kJ - 112 kJ/mol H2O) / 2
Calculating the result:
ΔHrxn = -154 kJ/mol Zn
Therefore, the heat change for the slow reaction of zinc with water is -154 kJ/mol Zn.