You reacted 3.5 g of Zn with 75 ml of 0.70 M HCl originally at 23 C and the final temperature of the mixture was 45 C. What is the [tex]$\Delta H_{rn}$[/tex] per mole of zinc reacted? (Check how much Zn reacted, i.e. it may not be limiting)
Answer (2)
Determine the limiting reactant: Calculate moles of Zn and HCl, and find that HCl is limiting.
Calculate heat absorbed by the solution: Use q = m c Δ T to find the heat absorbed.
Calculate the enthalpy change: Δ H = − q .
Calculate enthalpy change per mole of Zn: Divide Δ H by moles of Zn reacted to get − 262.99 kJ/mol .
Explanation
Gathering Information We are given the reaction of zinc (Zn) with hydrochloric acid (HCl), and we need to find the enthalpy change of the reaction ( Δ H r x n ) per mole of zinc reacted. First, let's gather all the given information:
Mass of Zn reacted = 3.5 g
Volume of HCl = 75 ml
Molarity of HCl = 0.70 M
Initial temperature = 23 °C
Final temperature = 45 °C
Balanced Chemical Equation The balanced chemical equation for the reaction between Zn and HCl is: Z n ( s ) + 2 H Cl ( a q ) → Z n C l 2 ( a q ) + H 2 ( g ) This equation tells us that 1 mole of Zn reacts with 2 moles of HCl.
Calculating Moles of Reactants Now, let's calculate the number of moles of Zn reacted: n Z n = m o l a r _ ma s s Z n ma s s Z n = 65.38 g/mol 3.5 g = 0.0535 mol And the number of moles of HCl initially present: n H Cl = M o l a r i t y H Cl × V o l u m e H Cl = 0.70 M × 0.075 L = 0.0525 mol
Determining the Limiting Reactant To determine the limiting reactant, we compare the mole ratio of Zn and HCl from the balanced equation. According to the balanced equation, 1 mole of Zn reacts with 2 moles of HCl. Therefore, we need to compare the ratio of moles: n Z n n H Cl = 0.0535 0.0525 = 0.981
Since this ratio is less than 2, HCl is the limiting reactant. This means that not all of the Zn will react. We need to calculate the moles of Zn that actually reacted based on the moles of HCl: m o l es _ Z n _ re a c t e d = 2 n H Cl = 2 0.0525 mol = 0.02625 mol
Calculating Heat Absorbed by the Solution Next, we calculate the heat absorbed by the solution using the formula: q = m × c × Δ T where:
m is the mass of the solution (assume the density of the solution is 1 g/ml, so the mass of the solution is 75 g)
c is the specific heat capacity of the solution (assume it's close to that of water, 4.184 J / g ∘ C )
Δ T is the change in temperature ( T f ina l − T ini t ia l = 45 ∘ C − 23 ∘ C = 22 ∘ C )
q = 75 g × 4.184 J/g ∘ C × 22 ∘ C = 6903.6 J
Calculating Enthalpy Change Now, we calculate the enthalpy change for the reaction: Δ H = − q = − 6903.6 J The negative sign indicates that the reaction is exothermic (heat is released).
Calculating Enthalpy Change per Mole of Zn Finally, we calculate the enthalpy change per mole of Zn reacted: Δ H r x n = m o l es _ o f _ Z n _ re a c t e d Δ H = 0.02625 mol − 6903.6 J = − 262994.29 J/mol Converting to kJ/mol: Δ H r x n = 1000 J/kJ − 262994.29 J/mol = − 262.99 kJ/mol
Final Answer The enthalpy change of the reaction per mole of zinc reacted is approximately -262.99 kJ/mol. This means that when 1 mole of zinc reacts with hydrochloric acid, 262.99 kJ of heat is released.
Final Answer Therefore, the Δ H r n per mole of zinc reacted is − 262.99 kJ/mol
Examples
Understanding enthalpy changes is crucial in various real-world applications. For instance, in designing chemical reactors, engineers need to know how much heat is released or absorbed during a reaction to maintain optimal operating conditions and prevent hazards. Similarly, in the development of new energy sources, such as biofuels or hydrogen fuel cells, knowing the enthalpy change helps evaluate the efficiency and sustainability of these technologies. In everyday life, understanding exothermic reactions (like the one in this problem) helps explain why certain chemical reactions, such as burning fuel, release heat and can be used for heating or generating power.
The enthalpy change per mole of zinc reacted is approximately -262.99 kJ/mol. This indicates that during the reaction, heat is released as zinc reacts with hydrochloric acid. Thus, the reaction is exothermic.
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