A piece of zinc reacts completely with hydrochloric acid, HCl(aq), to produce an aqueous solution of zinc chloride, ZnCl2(aq), and hydrogen gas.
a. Use the data shown below to determine the enthalpy of reaction per mole of zinc.
▲Hf of HCl(aq) = –167.2 kJ/mol
▲Hf of ZnCl2(aq) = –488.2 kJ/mol
Zn(s) + 2HCl(aq) → ZnCl2(aq) + H2(g)
b. What mass of zinc must be used for 123 kJ of heat energy to be given off?
a. dHrxn = (n*dHf of products) - (n*dHf of reactants)
You know dHf HCl and ZnCl2. Remember dHf H2 gas and Zn solid are zero.
Substitute and solve for the dH rxn. The approx answer is -150 kJ/mol but that's just a close estimate.
b, 1 mol Zn (about 65.4 g Zn) produces approx -150 kJ so we convert for grams needed for 123 kJ.
That's 65.4 g x (-123/-150) = ?
Post your work if you get stuck.
a. To determine the enthalpy of reaction per mole of zinc, we can use the enthalpy of formation values for the reactants and products.
The enthalpy change of a reaction can be calculated using the formula:
ΔHrxn = ∑ΔHf(products) - ∑ΔHf(reactants)
For the given reaction:
Zn(s) + 2HCl(aq) → ZnCl2(aq) + H2(g)
The enthalpy change can be calculated as follows:
ΔHrxn = ΔHf(ZnCl2(aq)) + ΔHf(H2(g)) - ΔHf(Zn(s)) - 2 * ΔHf(HCl(aq))
Substituting the given values:
ΔHrxn = -488.2 kJ/mol + 0 kJ/mol - 0 kJ/mol - 2 * (-167.2 kJ/mol)
ΔHrxn = -488.2 kJ/mol + 334.4 kJ/mol
ΔHrxn = -153.8 kJ/mol
Therefore, the enthalpy of reaction per mole of zinc is -153.8 kJ/mol.
b. To calculate the mass of zinc required for a given heat energy, we can use the equation:
q = m * ΔH
where q is the heat energy, m is the mass, and ΔH is the enthalpy change.
We are given that the heat energy released (q) is 123 kJ, and we need to find the mass of zinc (m).
Using the rearranged equation:
m = q / ΔH
Substituting the given values:
m = 123 kJ / (-153.8 kJ/mol)
Calculating the mass using the molar mass of zinc (65.38 g/mol):
m = (123,000 J / 1,000 kJ) / (-153.8 kJ/mol) * (1 mol / 65.38 g)
m ≈ -0.799 g
Since mass cannot be negative, we can conclude that we need approximately 0.799 g of zinc to release 123 kJ of heat energy.
a. To determine the enthalpy of reaction per mole of zinc, we need to calculate the enthalpy change (▲H) for the reaction using the given enthalpy of formation (▲Hf) values.
The enthalpy change for the reaction can be calculated using the following equation:
▲H = ∑▲Hf(products) - ∑▲Hf(reactants)
In this case, the reactants are Zn(s) and 2HCl(aq), and the products are ZnCl2(aq) and H2(g).
Using the given ▲Hf values:
∑▲Hf(products) = ▲Hf(ZnCl2(aq)) = -488.2 kJ/mol
∑▲Hf(reactants) = ▲Hf(HCl(aq)) + ▲Hf(Zn(s))
= -167.2 kJ/mol + 0 kJ/mol (since the ▲Hf of an element in its standard state is 0 kJ/mol)
Substituting these values into the equation, we can calculate ▲H:
▲H = -488.2 kJ/mol - (-167.2 kJ/mol)
= -488.2 kJ/mol + 167.2 kJ/mol
= -321 kJ/mol
Therefore, the enthalpy of reaction per mole of zinc is -321 kJ/mol.
b. To determine the mass of zinc required for 123 kJ of heat energy to be given off, we need to use the enthalpy change per mole of zinc from part a.
The molar enthalpy change for the reaction is given as -321 kJ/mol. This means that for every mole of zinc reacted, 321 kJ of heat energy is released.
To calculate the mass of zinc required for a specific amount of heat energy, we need to use the following equation:
Mass of zinc (g) = (Heat energy (kJ) / Molar enthalpy change (kJ/mol)) × Molar mass of zinc (g/mol)
The molar mass of zinc (Zn) is 65.38 g/mol.
Substituting the given values into the equation, we can solve for the mass of zinc:
Mass of zinc (g) = (123 kJ / -321 kJ/mol) × 65.38 g/mol
Simplifying the equation:
Mass of zinc (g) = -123 kJ × (1 mol / 321 kJ) × 65.38 g/mol
Mass of zinc (g) = -(123 kJ × 65.38 g) / (321 kJ)
≈ 25.15 g
Therefore, approximately 25.15 g of zinc must be used for 123 kJ of heat energy to be given off.