how many liters of CH4 measured at 23.4C and 768mmhg must be burned to provide the heat needed to vaporize 3.78L of water at 100C
q needed to vaporize H2O = 3780 g x delta Hvap = ??
To finish you need to know the heat released by CH4 at STP.
To solve this problem, we need to calculate the amount of heat required to vaporize the water and then find the amount of methane (CH4) needed to produce that much heat.
1. Calculate the heat required to vaporize the water:
The heat required to vaporize water can be calculated using the equation:
Q = m × ΔHvap
Where:
Q is the heat required
m is the mass of water
ΔHvap is the heat of vaporization
We know the volume of water given in liters, so we need to convert it to grams using its density at 100°C (which is approximately 1 g/mL).
Density of water at 100°C ≈ 1 g/mL
Therefore, the mass of water is:
mass = volume × density
mass = 3.78 L × 1 g/mL = 3.78 kg (since 1 kg = 1000 g)
The heat of vaporization of water is approximately 40.7 kJ/mol. Since the molar mass of water is 18.0 g/mol, we can calculate the heat required to vaporize the water:
Q = m × ΔHvap
Q = 3.78 kg × (40.7 kJ/mol / 18.0 g/mol)
Q ≈ 8.52 × 10^3 kJ
2. Calculate the amount of methane required:
Now, we need to find the amount of methane needed to produce this amount of heat. To do that, we need to use the balanced chemical equation for methane combustion:
CH4 + 2O2 -> CO2 + 2H2O
According to the equation, 1 mole of CH4 produces 2 moles of H2O. So, we can calculate the number of moles of water produced:
moles of H2O = moles of CH4 × (2 moles of H2O / 1 mole of CH4)
Since we are given the volume of methane in liters, we need to convert it to moles using the ideal gas law. The ideal gas law equation is:
PV = nRT
Where:
P is the pressure
V is the volume
n is the number of moles
R is the ideal gas constant
T is the temperature in Kelvin
We need to convert the temperature from Celsius to Kelvin by adding 273.15:
T = 23.4°C + 273.15 = 296.55 K
Given that the pressure is 768 mmHg, we need to convert it to atmosphere (atm) because the ideal gas constant R = 0.0821 L × atm / (mol × K):
P = 768 mmHg × (1 atm / 760 mmHg)
Now, we can rearrange the ideal gas law equation to solve for the number of moles:
n = PV / (RT)
Substitute the values into the equation to find the number of moles of CH4:
n = (P × V) / (R × T)
Finally, we can calculate the number of moles of water produced:
moles of H2O = n × (2 moles of H2O / 1 mole of CH4)
3. Convert moles of water into liters of CH4:
Since 1 mole of CH4 has a volume of 22.4 L (at standard temperature and pressure), we can convert the moles of water into liters of CH4:
liters of CH4 = moles of H2O × (1 mole of CH4 / 2 moles of H2O) × 22.4 L/mole
By following these steps, you can calculate the number of liters of CH4 needed to provide the heat required to vaporize 3.78L of water at 100°C.