Propane gas is used to heat a tank of water. If the tank contains 200 L of water, what mass of propane will be required to raise its temperature from 20 degrees C to 65 degrees C. The heat of combustion for propane is -2220 kJ/mol.
747.9
To calculate the mass of propane required to raise the temperature of the water, we need to follow these steps:
Step 1: Calculate the heat required to raise the temperature of water:
The heat required (q) can be calculated using the formula:
q = m × Cp × ΔT
Where:
- m is the mass of water
- Cp is the specific heat capacity of water (4.18 J/g°C)
- ΔT is the change in temperature
Step 2: Convert the heat into kilojoules:
Since the heat of combustion for propane is provided in kJ/mol, we need to convert the heat from the previous step into kilojoules (kJ).
Step 3: Calculate the moles of propane:
To calculate the moles of propane, we need to use the molar mass of propane.
Step 4: Finally, calculate the mass of propane:
Using the moles of propane calculated in the previous step, we can find the mass of propane using the molar mass of propane (44.1 g/mol).
Let's perform the calculations:
Step 1:
q = m × Cp × ΔT
q = 200 L × 1000 g/L × 4.18 J/g°C × (65°C - 20°C)
q = 200000 g × 4.18 J/g°C × 45°C
q = 37620000 J
Step 2:
Convert the heat into kilojoules:
q = 37620000 J ÷ 1000 = 37620 kJ
Step 3:
To calculate the moles of propane, we can use the equation:
q = n × ΔH
Where:
- n is the number of moles of propane
- ΔH is the heat of combustion for propane (-2220 kJ/mol)
n = q ÷ ΔH
n = 37620 kJ ÷ -2220 kJ/mol
n ≈ -16.92 mol
Step 4:
The molar mass of propane is approximately 44.1 g/mol. We can use this to calculate the mass of propane:
Mass of propane = n × molar mass of propane
Mass of propane = -16.92 mol × 44.1 g/mol
Mass of propane ≈ -746.77 g
Note: The negative sign indicates that the reaction is exothermic. However, mass cannot be negative in real life. Therefore, the mass of propane required to raise the temperature of the water from 20°C to 65°C is approximately 746.77 g.
To find the mass of propane required to heat the tank of water, we need to use the equation:
q = m × C × ΔT
Where:
q = heat energy
m = mass of the substance (propane)
C = specific heat capacity
ΔT = change in temperature
First, let's find the heat energy required to raise the temperature of the water. The equation for heat energy is:
q = m × C × ΔT
Where:
q = heat energy
m = mass of the substance (water)
C = specific heat capacity of water (4.18 J/g°C)
ΔT = change in temperature
Substituting the given values:
q = (200 L × 1000 g/L) × (4.18 J/g°C) × (65°C - 20°C)
q = 200000 g × 4.18 J/g°C × 45°C
q = 3771000 J
We have calculated the heat energy required to raise the temperature of the water to be 3,771,000 J.
Next, we can use the heat of combustion of propane to find the mass of propane required. The equation for heat energy in terms of moles is:
q = n × ΔH
Where:
q = heat energy (3771000 J)
n = number of moles of propane
ΔH = heat of combustion for propane (-2220 kJ/mol)
First, let's convert the heat of combustion from kJ/mol to J/mol:
ΔH = -2220 kJ/mol × 1000 J/kJ
ΔH = -2,220,000 J/mol
Rearranging the equation:
n = q / ΔH
n = 3771000 J / -2,220,000 J/mol
Now, let's calculate the number of moles of propane required:
n = -1.7 mol
Finally, we can calculate the mass of propane required using the molar mass of propane, which is approximately 44 g/mol:
mass = n × molar mass
mass = -1.7 mol × 44 g/mol
Therefore, the mass of propane required to heat the tank of water is approximately -74.8 g. However, a negative mass is not physically meaningful in this context. It is possible that an error occurred during the calculations, so please double-check the given values and equations used.
How much heat do you need?
q = mass x specific heat water x (Tfinal-Tinitial).
2220 kJ/mol propane x ymols = q
Solve for y moles.
Then y moles propane x molar mass propane = grams propane.
Check my thinking.