Question

Reactive metals such as magnesium react readily with acids in aqueous solution. 2.06 g of Mg is added to 95.2 mL of a 1.00 M aqueous solution of HCl, producing an increase in temperature of 7.6°C. If the molar heat capacity of 1.00 M HCl is the same as that for water [cP = 75.3 J/(mol∙°C)], what is ΔHrxn?

Answer 1

To find the ∆Hrxn for the reaction of magnesium with hydrochloric acid, one must calculate the heat released during the reaction using the mass, specific heat capacity,

Step-by-step explanation:

The question asks to calculate the ∆Hrxn (enthalpy change) for the reaction of magnesium with hydrochloric acid.

Given that 2.06 g of Mg is reacted with 1.00 M HCl aqueous solution, which produces a temperature increase of 7.6°C, we can calculate the heat change (q) using the mass of the HCl solution, its specific heat capacity (cp), and the temperature change (∆T).

First, we convert the solution's volume to mass (assuming the density of water, which is 1 g/mL). Thus, 95.2 mL HCl solution has a mass of 95.2 g.

Using the formula q = m•c•∆T, where m is the mass, c is the specific heat capacity, and ∆T is the temperature change, the heat (q) released can be calculated. The molar heat capacity (75.3 J/(mol•°C)) is multiplied by the moles of solution to get the specific heat capacity (c).

To find the moles of magnesium, we use the molar mass of Mg (24.305 g/mol), which gives us moles of Mg = 2.06 g / 24.305 g/mol.

Then, we can use the stoichiometry of the reaction, which states that 1 mole of Mg reacts with 2 moles of HCl, to determine the moles of HCl reacted. Here, we assume that all the Mg reacts.

Finally, ∆Hrxn can be found by dividing the heat (q) by the moles of Mg reacted. Since the reaction is exothermic, ∆Hrxn should be negative, indicating that heat is released.