Finding the mass

Question

Liquid sodium is being considered as an engine coolant. How many grams of liquid sodium (minimum) are needed to absorb 4.10 MJ of energy (in the form of heat) if the temperature of the sodium is not to increase by more than 10.0 °C? Use CP = 30.8 J/(K·mol) for Na(l) at 500 K.  

 

Please help me. I can not figure this out and I am down to my last guess. 

Answer 1

The heat absorbed by the sodium is given by the formula

 

Q=n c_p ΔT,

 

where n is the number of moles, c_p the molar heat capacity at constant pressure, and ΔT the temperature change in Kelvin (which equals the temperature change in °Celsius). To find the mass, we first find the number of mols:

 

n=Q/(c_p ΔT)=4.1*10⁶J/(30.8*10 J/mol) =13,300 mol

 

Look up the molar mass of sodium, M=23 g/mol, and find the mass of sodium required is

 

m=23 g/mol *13,300mol = 306000 g =31 kg