Question

A 0.158 g sample of magnesium metal reacts completely with 100.0 mL of 1.0 M hydrochloric acid in a coffee cup calorimeter. The temperature of the solution rose from 25.6°C to 32.8°C. What is ∆Hrxn? Assume the specific heat of the solution is 4.184 J/mol-K and the density is 1.0 g/mL.

Answer 1

Step-by-step explanation:

The given data is as follows.

mass = 0.158 g, volume = 100 ml

Molarity = 1.0 M,
`\Delta T` =
`(32.8 - 25.6)^(o)C = 7.2^(o)C`

The given reaction is as follows.

`Mg(s) + 2HCl(aq) \rightarrow MgCl_(2)(aq) + H_(2)(g)`

So, moles of magnesium will be calculated as follows.

No. of moles =
`\frac{mass}{\text{molar mass}}`

=
`(0.158 g)/(24.305 g/mol)`

=
`6.5 * 10^(-3)`

= 0.0065 mol

Now, formula for heat released is as follows.

Q =
`m * C * \Delta T`

=
`\text{volume} * \text{density} * C * \Delta T`

=
`100 ml * 1.0 g/ml * 4.184 * 7.2^(o)C`

= 3010.32 J

Hence, heat of reaction will be calculated as follows.

`\Delta H_(rxn) = \frac{\text{-heat released}}{\text{moles of Mg}}`

=
`(3010.32 J)/(0.0065 mol)`

= -4.63 J/mol

or, =
`-463 * 10^(-5) kJ/mol` (as 1 kJ = 1000 J)

Thus, we can conclude that heat of given reaction is
`-463 * 10^(-5)` kJ/mol.