What is the volume of the bomb calorimeter?

Question

100 mL of water underwent decomposition inside a bomb calorimeter to produce hydrogen and oxygen gas. After all of the water was decomposed, the temperature inside the bomb calorimeter was increased to 375.50 K and the pressure was 2.5 atm. What is the volume of the bomb calorimeter?

Answer 1

Step 1: Use the equation PV = nRT (ideal gas law) and solve for volume.

V = nRT / P

n = 100mL of water (See step 2)

R = 0.082057 (L * atm)/(mol * K)

T = 375.50K

P = 2.5 atm

Step 2: Use the density and molecular weight of water to convert 100mL of water to moles of water.

density = p = 1 g/mL

Molecular Weight = MW = 18.02 g/mol

100 mL of water * [1 g of water / 1 mL of water] * [1 mol of water / 18.02 g of water] = 100/18.02 = 5.55 mol of water

Step 3: Use the newly acquired moles of water to calculate the volume of the bomb calorimeter.

V = 5.55*0.082057*375.50/2.5 = 68.4 L