Caculate the volume of CO2 gas given off at 756 mm Hg and 23C when 150 kg of limestone(CaCO3) is heated until it decomposes according to the following reaction:CaCO3(s)=CaO(s)+CO2(g)
CaCO3 ==> CaO + CO2
mols CaCO3 = grams/molar mass = 150,000 x molar mass CaCO3 = ?
Convert mols CaCO3 to mols CO2\]
Them convert mols CO2 to volume in L at the conditions listed by using PV = nRT.
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To calculate the volume of CO2 gas given off, we need to use the ideal gas law equation: PV = nRT. In this equation, P represents the pressure of the gas, V represents the volume of the gas, n represents the number of moles of gas, R is the ideal gas constant, and T represents the temperature of the gas in Kelvin.
First, we need to determine the number of moles of CO2 gas produced from the limestone. To do this, we must convert the given mass of limestone to moles using its molar mass.
The molar mass of CaCO3 is calculated as follows:
Molar mass of Ca = 40.08 g/mol
Molar mass of C = 12.01 g/mol
Molar mass of O = 16.00 g/mol
To calculate the molar mass of CaCO3, we add the molar masses of Ca, C, and 3O together:
Molar mass of CaCO3 = (40.08 g/mol) + (12.01 g/mol) + (3 * 16.00 g/mol) = 100.09 g/mol.
We then convert the given mass of limestone (150 kg) to grams:
Mass of limestone = 150 kg * 1000 g/kg = 150,000 g.
Next, we calculate the number of moles of CaCO3:
Number of moles of CaCO3 = Mass of limestone / Molar mass of CaCO3 = 150,000 g / 100.09 g/mol.
Now we can determine the volume of CO2 gas using the ideal gas law. However, we first need to convert the given pressure from mm Hg to atm and the given temperature from Celsius to Kelvin.
To convert pressure from mm Hg to atm, we divide by 760:
Pressure (in atm) = 756 mm Hg / 760 mm Hg/atm.
To convert temperature from Celsius to Kelvin, we add 273.15:
Temperature (in Kelvin) = 23 degrees Celsius + 273.15.
Now, we substitute the values into the ideal gas law equation:
PV = nRT.
We know the pressure (in atm), the volume (which we want to find), the number of moles (which we calculated), the ideal gas constant (R = 0.0821 L·atm/(mol·K)), and the temperature (in Kelvin).
Therefore, we can rearrange the ideal gas law equation to solve for the volume (V):
V = (nRT) / P.
Substituting the values into the equation, we get:
V = (number of moles of CO2) * (R constant) * (temperature in Kelvin) / (pressure in atm).