# Question 2cc3c

Jul 7, 2017

Here's what I got.

#### Explanation:

The idea here is that the heat given off by the combustion of the sample will be equal to the heat absorbed by the calorimeter.

The calorimeter has a heat capacity of ${\text{3024 J" ""^@"C}}^{- 1}$, which means that it takes $\text{3024 J}$ of heat to increase its temperature by ${1}^{\circ} \text{C}$.

In your case, the temperature of the calorimeter increased by ${3.337}^{\circ} \text{C}$, which implies that the calorimeter absorbed

3.337 color(red)(cancel(color(black)(""^@"C"))) * "3024 J"/(1color(red)(cancel(color(black)(""^@"C")))) = "10,091.1 J"

Convert this to kilojoules

$\text{10,091.1" color(red)(cancel(color(black)("J"))) * "1 kJ"/(10^3color(red)(cancel(color(black)("J")))) = "10.091 kJ}$

Now, you know that the calorimeter absorbed $\text{10.091 kJ}$ of heat, so it must mean that the reaction gave off $\text{10.091 kJ}$ of heat.

Moreover, you know that this much heat was given off when $\text{0.4075 g}$ of magnesium underwent combustion. You can thus say that the heat released when $\text{1 g}$ of magnesium undergoes combustion is equal to

1 color(red)(cancel(color(black)("g"))) * "10.091 kJ"/(0.4075 color(red)(cancel(color(black)("g")))) = "24.76 kJ"

Since this heat is being given off, you can say that the enthalpy change of combustion of magnesium will be equal to

DeltaH_"comb" = color(darkgreen)(ul(color(black)(- "24.76 kJ g"^(-1))))

The minus sign is used to symbolize heat given off.

Finally, to convert this to kilojoules per mole, use the molar mass of magnesium

-24.76 color(white)(.)"kJ"/color(red)(cancel(color(Black)("g"))) * (24.305 color(red)(cancel(color(Black)("g"))))/("1 mole Mg") = color(darkgreen)(ul(color(black)(-"601.8 kJ mol"^(-1))))#

The answers are rounded to four sig figs.