The bottled butane gas is installed in an oven that can supply 0.125 g/hr .In a kitchen room of volume 32 m^3 (volume of air), the oven is made to operate for 2 hours. Assuming the kitchen room is closed, what is the mole composition of the atmosphere in the kitchen when combustion ceases. Conclude.
The average mole composition of air under the given conditions is:
Oxygen 21%
Nitrogen 79%
Carbon dioxide 0.03%
To find the mole composition of the atmosphere in the kitchen after combustion ceases, we need to consider the chemical reaction that occurs during combustion of butane gas. The balanced chemical equation for the combustion of butane is:
2 C4H10 + 13 O2 -> 8 CO2 + 10 H2O
From the equation, we can see that for every 2 moles of butane (C4H10), we need 13 moles of oxygen (O2) to fully combust the butane. In this case, the butane is being supplied at a rate of 0.125 g/hr, and it operates for 2 hours. Let's calculate the number of moles of butane consumed:
0.125 g/hr * 2 hr = 0.25 g
Now, we need to convert the mass of butane to moles using its molar mass. The molar mass of butane (C4H10) is approximately 58.12 g/mol:
0.25 g * (1 mol / 58.12 g) = 0.0043 mol
Since we need 2 moles of butane to fully combust with 13 moles of oxygen, we can calculate the number of moles of oxygen required:
0.0043 mol butane * (13 mol O2 / 2 mol butane) = 0.028 mol O2
Now that we know the number of moles of oxygen consumed during combustion, we can find the new composition of the atmosphere in the kitchen. Initially, the mole composition of air in the kitchen was:
Oxygen: 21% = 0.21
Nitrogen: 79% = 0.79
Carbon dioxide: 0.03% = 0.0003
The number of moles of oxygen initially in the kitchen was:
0.21 * 32 m^3 = 6.72 mol
After combustion, the number of moles of oxygen remaining in the kitchen is:
6.72 mol - 0.028 mol = 6.692 mol
The mole composition of the atmosphere in the kitchen after combustion ceases is:
Oxygen: (6.692 mol / (6.692 mol + 0.79 mol) ) = 0.894
Nitrogen: 0.79 mol / (6.692 mol + 0.79 mol) = 0.106
Carbon dioxide: 0.0003
So, the mole composition of the atmosphere in the kitchen after combustion ceases is approximately:
Oxygen: 89.4%
Nitrogen: 10.6%
Carbon dioxide: 0.03%
To find the mole composition of the atmosphere in the kitchen after combustion ceases, we need to calculate the amount of butane gas consumed during the 2 hours of operation and the resulting amounts of carbon dioxide and water vapor produced.
Step 1: Calculate the amount of butane gas consumed:
Given that the oven supplies 0.125 g of butane gas per hour, the total amount of butane consumed during 2 hours is:
0.125 g/hr * 2 hr = 0.25 g
Step 2: Calculate the amount of carbon dioxide produced:
From the balanced combustion equation for butane:
2 C4H10 + 13 O2 -> 8 CO2 + 10 H2O
We can see that for every mole of butane burned, 8 moles of carbon dioxide are produced.
The molar mass of butane (C4H10) is 58.12 g/mol.
0.25 g of butane is equivalent to 0.25 g / 58.12 g/mol = 0.0043 moles of butane.
Therefore, the amount of carbon dioxide produced is:
0.0043 moles of butane * 8 moles of CO2/mole of butane = 0.0344 moles of CO2
Step 3: Calculate the mole composition of the atmosphere in the kitchen after combustion ceases:
Given that the volume of the kitchen room is 32 m^3 and assuming it is a closed system, we can use the ideal gas law to relate moles of gas to volume.
The ideal gas law equation is:
PV = nRT
Where:
P is the pressure of the gas (assumed constant)
V is the volume of the gas (32 m^3)
n is the number of moles of gas
R is the ideal gas constant (0.0821 L·atm/mol·K)
T is the temperature of the gas (assumed constant)
We can rearrange the equation to solve for n:
n = PV / RT
Assuming room temperature around 25°C (298 K) and atmospheric pressure (around 1 atm), we can substitute these values into the equation to find the total number of moles of gas in the kitchen room.
n = (1 atm) * (32 m^3) / ((0.0821 L·atm/mol·K) * (298 K))
n = 1.36 moles
Given that the mole composition of air is:
Oxygen 21% (0.21 moles)
Nitrogen 79% (1.07 moles)
Carbon dioxide 0.03% (0.000408 moles)
After combustion ceases, the mole composition changes due to the addition of carbon dioxide from the butane combustion. Therefore, the new mole composition of the atmosphere in the kitchen is:
Oxygen: 0.21 moles
Nitrogen: 1.07 moles
Carbon dioxide: 0.0344 moles (initial CO2) + 0.000408 moles (from butane combustion) = 0.0348 moles
So, the final mole composition of the kitchen's atmosphere is approximately:
Oxygen: 15%
Nitrogen: 79%
Carbon dioxide: 6%
In conclusion, after combustion ceases, the mole composition of the atmosphere in the kitchen changes with reduced oxygen levels and increased carbon dioxide levels. However, the percentage composition of nitrogen remains the same.