Question

Question #2cc3c

Answer 1

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 `"3024 J" ""^@"C"^(-1)`, which means that it takes `"3024 J"` of heat to increase its temperature by `1^@"C"`.

In your case, the temperature of the calorimeter increased by `3.337^@"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

`"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 `"10.091 kJ"` of heat, so it must mean that the reaction gave off `"10.091 kJ"` of heat.

Moreover, you know that this much heat was given off when `"0.4075 g"` of magnesium underwent combustion. You can thus say that the heat released when `"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.