Question

Question #23703

Answer 1

Heat lost equals heat gained.
The hot metal transfers heat to the cooler water until both temperatures are equal. The equation for heat gained or lost is
Q = mcΔT. Q is the heat, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
In the case of the metal mass, Q is lost. Water gains the heat. So:
36.835 g x c x (100-29)°C = 30 g x 4.186 J/g°C x (29.0-22.1)°C
The metal's specific heat capacity is 0.331 J/g°C.

 To convert this to a molar form you will need to identify the metal, most likely using the specific heat value. However, I haven't been able to find a metal that matches this value. The closest elements I found are arsenic, germanium, and selenium. 
 Convert one gram of the element to a molar amount. ( **For example**, 1 g of Na would be 1/22.99 = 0.0435 mol Na.) Substitute the amount you determine for your sample into the specific heat value and calculate the value of 0.331/(# of mol).  If the metal were sodium (it isn't), you would have 0.331J/0.0435 mol °C = 7.61 J/mol°C.