Question

0.158 g of a mystery molecule is placed into a bomb calorimeter that has a heat capacity of 1650 J/C. After the sample is combusted the temperature of the calorimeter increased by 2.54 C. Determine the molar mass of the mystery molecule if the enthalpy of combustion for one mole is 2960 kJ/mol

Answer 1

Answer: The molar mass of the mystery element is 111.27 g/mol

Explanation:

To calculate the heat absorbed by the calorimeter, we use the equation:

$q=c\Delta T$

where,

q = heat absorbed

c = heat capacity of calorimeter = 1650 J/°C

$\Delta T$ = change in temperature = $2.54^oC$

Putting values in above equation, we get:

$q=1650J/^oC\times 2.54^oC=4191kJ$

Heat absorbed by the calorimeter will be equal to the heat released by the reaction.

Sign convention of heat:

When heat is absorbed, the sign of heat is taken to be positive and when heat is released, the sign of heat is taken to be negative.

To calculate the number of moles of the mystery molecule, we use the equation:

$\Delta H_{rxn}=\frac{q}{n}$

where,

q = amount of heat released = -4191 J

n = number of moles = ? moles

$\Delta H_{rxn}$ = enthalpy change of the reaction = -2960 kJ/mol = -2960000 J/mol    (Conversion factor = 1 kJ = 1000 J)

Putting values in above equation, we get:

$-2960000=\frac{-4191J}{n}\\\\n=\frac{-4191}{-2960000}=0.00142mol$

To calculate the number of moles, we use the equation:

$\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}$

Given mass of mystery molecule = 0.158 g

Moles of mystery molecule = 0.00142 mol

Putting values in above equation, we get:

$0.00142mol=\frac{0.158g}{\text{Molar mass of mystery molecule}}\\\\\text{Molar mass of mystery molecule}=\frac{0.158}{0.00142}=111.27g/mol$

Hence, the molar mass of the mystery element is 111.27 g/mol