Calcium oxide (CaO), an important ingredient in cement, is produced by decomposing calcium carbonate (CaCO3) at high temperature:
CaCO3(s) → CaO(s) + CO2(g)
In one particular reaction, 40 g of CaCO3 is heated at 750°C in a 5.0 L vessel. The pressure of CO2 is 0.12 atm after 4.0 minutes. What is the average rate of CO2 production in moles per minute during the 4 minutes?
If you assume this rate of decomposition remains constant, how many minutes will it take for the entire sample of CaCO3 to decompose?
Help?
To find the average rate of CO2 production in moles per minute, we first need to determine the number of moles of CO2 produced during the 4 minutes.
Step 1: Calculate the number of moles of CO2 produced.
To do this, we need to use the ideal gas equation:
PV = nRT
Where:
P is the pressure of CO2 in atm (0.12 atm)
V is the volume of the vessel in liters (5.0 L)
n is the number of moles of CO2 produced (unknown)
R is the ideal gas constant (0.0821 L·atm/mol·K)
T is the temperature in Kelvin (750°C = 1023.15 K)
Rearranging the equation to solve for n, we get:
n = PV / RT
Plugging in the values, we have:
n = (0.12 atm) * (5.0 L) / (0.0821 L·atm/mol·K * 1023.15 K)
Calculating this gives us:
n = 0.0073 mol
So, during the 4 minutes, 0.0073 moles of CO2 were produced.
Step 2: Calculate the average rate of CO2 production in moles per minute.
To find the average rate, we divide the number of moles produced by the time:
Average rate = Number of moles / Time
Plugging in the values, we have:
Average rate = 0.0073 mol / 4.0 min
Calculating this gives us:
Average rate = 0.0018 mol/min
Therefore, the average rate of CO2 production during the 4 minutes is 0.0018 moles per minute.
Now, to determine the time it takes for the entire sample of CaCO3 to decompose, we can use the ratio of the number of moles of CaCO3 to the rate of CO2 production.
Step 1: Calculate the number of moles of CaCO3.
To do this, we use the molar mass of CaCO3, which is 100.09 g/mol.
So, for 40 g of CaCO3:
Number of moles of CaCO3 = Mass / Molar mass
Number of moles of CaCO3 = 40 g / 100.09 g/mol
Calculating this gives us:
Number of moles of CaCO3 = 0.3996 mol
Step 2: Calculate the time required for decomposition.
To find the time, we divide the number of moles of CaCO3 by the rate of CO2 production:
Time = Number of moles of CaCO3 / Rate
Plugging in the values, we have:
Time = 0.3996 mol / 0.0018 mol/min
Calculating this gives us:
Time = 222 minutes
Therefore, it will take approximately 222 minutes for the entire sample of CaCO3 to decompose if the rate of decomposition remains constant.