The combustion of 0.0222g of isooctane vapor, C8H18(g), at constant pressure raises the temperature of a calorimeter 0.400 degrees C. The heat capacity of the calorimeter and water combined is 2.48kJ/degrees C. Find the molar heat of combustion of gaseous isooctane.

The balanced cchemical equation is:
C8H18(g)+12(1/2)O2(g) -> 8CO2(g)+9H2O(l)

q = 2480 J/C x 0.400 C = ?

q/gram = q/0.0222
q/mol = q/g x molar mass = 9q/0.0222) x molar mass

I got the answer 5,110 kJ/mol. But the answer is supossed to be negative. Why should it be negative?

Because it's an exothermic reaction. dHrxn = - (q/0.0222) x molar mass

The water T was raised which means it absorbed heat; therefore, the heat had to come from the reaction and that makes it exotherrmic.

To find the molar heat of combustion of gaseous isooctane (C8H18), we can use the following equation:

q = CΔT

Where:
q is the heat transferred to the calorimeter and water (Joules),
C is the heat capacity of the calorimeter and water combined (J/°C),
ΔT is the change in temperature (°C).

First, convert the mass of isooctane vapor (0.0222 g) to moles. To do this, we need to know the molar mass of isooctane (C8H18). The molar mass is the sum of the atomic masses of all atoms in the molecule.

Molar mass of C8H18 = (12 g/mol x 8) + (1 g/mol x 18) = 114 g/mol

Now, determine the number of moles of isooctane by dividing the mass by the molar mass:

Number of moles of C8H18 = 0.0222 g / 114 g/mol

Next, we need to calculate the heat transferred to the calorimeter and water (q). We can use the equation:

q = CΔT

Here, the heat capacity (C) is given as 2.48 kJ/°C. Convert this to Joules:

C = 2.48 kJ/°C x 1000 J/1 kJ = 2480 J/°C

The change in temperature (ΔT) is 0.400 °C, as given in the problem.

Substitute the given values into the equation:

q = (2480 J/°C) x (0.400 °C)

Now, we have the total heat transferred to the calorimeter and water (q).

To find the molar heat of combustion of gaseous isooctane, we need to divide the heat transferred (q) by the number of moles of isooctane:

Molar heat of combustion of isooctane = q / number of moles of C8H18

Substitute the calculated value of q and the number of moles of C8H18 into the equation to get the molar heat of combustion of isooctane.