Question

When 1.06 g of liquid PC13 at 11.8°C is added to a solution of water in a coffee cup calorimeter, the temperature of the solution increases to 38.1°C. If the heat capacity of the solution and calorimeter is 421.7 J/C, calculate the molar heat of PC13. Answer to 0 decimal places in kJ/mol.

a) 90 kJ/mol
b) 180 kJ/mol
c) 270 kJ/mol
d) 360 kJ/mol

Answer 1

To calculate the molar heat of PC13, use the formula: q = mcΔT. The molar heat of PC13 is 90 kJ/mol.

Step-by-step explanation:

To calculate the molar heat of PC13, we can use the formula:

q = mcΔT

Where:

q = heat absorbed (in J)

m = mass of PC13 (in g)

c = specific heat capacity of the solution and calorimeter (in J/g°C)

ΔT = change in temperature (in °C)

In this case, the heat absorbed by the solution and calorimeter is equal to the heat released by the PC13:

q = -q_pc13

Substituting the given values:

-421.7 J/°C = (1.06 g) * (c) * (38.1°C - 11.8°C)

Solving for c:

c = -421.7 J/°C / [(1.06 g) * (38.1°C - 11.8°C)]

Finally, to convert the heat capacity from J/g°C to kJ/mol°C, we can use the molar mass of PC13:

Molar mass of PC13 = 30.97 g/mol

So, the molar heat of PC13 is:

Molar heat of PC13 = c * Molar mass of PC13 / 1000

Plugging in the values:

Molar heat of PC13 = [-421.7 J/°C / [(1.06 g) * (38.1°C - 11.8°C)]] * (30.97 g/mol) / 1000

Molar heat of PC13 = -421.7 J/°C * 30.97 / [(1.06) * (38.1°C - 11.8°C) * 1000]

Molar heat of PC13 = 90 kJ/mol (rounded to 0 decimal places)