# Consider the following reaction: 2Mg(s) + O_2(g) -> 2MgO(s), DeltaH = -1204kJ. Is this reaction exothermic or endothermic? How do you calculate the amount of heat transferred when 2.4 grams of Mg(s) reacts at constant pressure?

## How many grams of MgO are produced during an enthalpy change of -96.0 kJ? How many kilojoules of heat are absorbed when 7.50 g of MgO(s) is decomposed into Mg(s) and ${O}_{2} \left(g\right)$ at constant pressure?

May 15, 2017

This reaction as written is clearly $\text{exothermic..............}$

#### Explanation:

We has..............

$2 M g \left(s\right) + {O}_{2} \left(g\right) \rightarrow 2 M g O \left(s\right)$ $\Delta {H}^{\circ} \text{_"rxn} = - 1204 \cdot k J \cdot m o {l}^{-} 1$ $\left(i\right)$

To make the arithmetic a bit easier we could write........

$M g \left(s\right) + \frac{1}{2} {O}_{2} \left(g\right) \rightarrow M g O \left(s\right)$ $\Delta {H}^{\circ} \text{_"rxn} = - 602 \cdot k J \cdot m o {l}^{-} 1$ $\left(i i\right)$

I am CLEARLY free to do this because $\Delta {H}^{\circ}$ is quoted $\text{per mole of reaction as written..........}$

And so we combust a $\frac{2.4 \cdot g}{24.3 \cdot g \cdot m o {l}^{-} 1} = 0.0988 \cdot m o l$ quantity of metal.

And thus for the given molar quantity of magnesium, $\Delta {H}_{\text{rxn}} = 0.0988 \cdot \cancel{m o l} \times - 602 \cdot k J \cdot \cancel{m o {l}^{-} 1} = - 59.5 \cdot k J$

So, in effect, we have treated enthalpy as a stoichiometric product of the reaction (which indeed it is!). And if $- 96.0 \cdot k J$ energy are generated, with respect to $M g O$, this requires a molar quantity of $\frac{- 96.0 \cdot k J}{- 602 \cdot k J \cdot m o {l}^{-} 1} = 0.159 \cdot m o l$ of rxn $\left(i i\right)$, i.e. $0.159 \cdot m o l \times 24.3 \cdot g \cdot m o {l}^{-} 1 = 3.88 \cdot g$ with respect to magnesium metal.

And when $7.5 \cdot g$ metal are combusted, this should result in a heat output of ..........................

$\frac{7.5 \cdot g}{24.3 \cdot g \cdot m o {l}^{-} 1} \times - 602 \cdot k J \cdot m o {l}^{-} 1 = - 185.8 \cdot k J$

Finally, you have proposed that a given mass of $M g O$ is decomposed to magnesium metal, and oxygen gas. Clearly, the energy here must be supplied to the system for decomposition. Can you handle this yourself?