100.0 g of copper(II) carbonate (molar mass = 123.56 g/mol) was heated until it decomposed completely. The gas was collected and cooled to room temperature and normal pressure (25¨¬C and 1.00 atm). What volume of carbon dioxide was produced? The reaction is: CuCO3(s) ¡æ CuO(s) + CO2(g)
2.310
To calculate the volume of CO2 produced, we first need to find the number of moles of CO2 produced using stoichiometry:
1 mol CuCO3 produces 1 mol CO2
So, the number of moles of CO2 produced can be calculated as:
mol CO2 = mol CuCO3 = 100.0 g / 123.56 g/mol = 0.809 mol
Next, we can use the ideal gas law to calculate the volume of CO2 at room temperature and normal pressure:
PV = nRT
where:
P = pressure = 1.00 atm
V = volume (unknown)
n = number of moles = 0.809 mol
R = gas constant = 0.0821 L·atm/mol·K
T = temperature = 25°C + 273.15 = 298.15 K
Plugging in these values and solving for V, we get:
V = nRT/P = (0.809 mol)(0.0821 L·atm/mol·K)(298.15 K)/(1.00 atm) = 17.54 L
Therefore, 17.54 L of CO2 was produced.
To find the volume of carbon dioxide gas produced, we can use the ideal gas law equation: PV = nRT.
First, let's calculate the number of moles of carbon dioxide produced using the given mass of copper(II) carbonate and its molar mass.
Step 1: Calculate the number of moles of copper(II) carbonate.
n(CuCO3) = mass(CuCO3) / molar mass(CuCO3)
n(CuCO3) = 100.0 g / 123.56 g/mol
n(CuCO3) = 0.8096 mol
Step 2: Since the balanced chemical equation is 1:1 for the formation of carbon dioxide, the number of moles of CO2 produced is also 0.8096 mol.
Now, let's determine the volume of carbon dioxide.
Step 3: Convert the temperature from Celsius to Kelvin.
T = 25°C + 273.15
T = 298.15 K
Step 4: Plug in the values into the ideal gas law equation and solve for volume(V).
PV = nRT
V = (nRT) / P
Given:
n = 0.8096 mol
R = 0.0821 L∙atm/mol∙K (ideal gas constant)
T = 298.15 K
P = 1.00 atm
V = (0.8096 mol × 0.0821 L∙atm/mol∙K × 298.15 K) / 1.00 atm
V ≈ 19.95 L
Therefore, approximately 19.95 liters of carbon dioxide gas were produced.