A 5.000g sample of a dry mixture of potassium hydroxide, potassium carboate and potassium chloride is reacted with 0.100 L of 2.00-molar HCl solution. A 249.0 mL sample of dry carbon dioxide gas, measured at 22.0 degree Celsius and 740.0 torr, is obtained from this reaction. What was the percentage of potassium carbonate in the mixture?
Use PV = nRT to solve for n = mols CO2.
mols CO2 = mols K2CO3
Then grams K2CO3 = mols K2CO3 x molar mass K2CO3.
%K2CO3 = (grams K2CO3/mass sample)*100 = ?
27.68%
To find the percentage of potassium carbonate in the mixture, we need to calculate the number of moles of carbon dioxide produced and then use stoichiometry to find the moles of potassium carbonate.
Step 1: Convert 249.0 mL of carbon dioxide gas to moles.
We can use the ideal gas law equation: PV = nRT
V = 249.0 mL = 0.249 L
T = 22.0°C = 295.15 K
P = 740.0 torr
R is the ideal gas constant, which is 0.08206 L·atm/(K·mol).
Using the equation PV = nRT, we can solve for n (number of moles):
n = PV / RT
n = (740.0 torr * 0.249 L) / (0.08206 L·atm/(K·mol) * 295.15 K)
Step 2: Calculate the number of moles of potassium carbonate.
From the balanced chemical equation, we know that 1 mole of carbon dioxide is produced for every 1 mole of potassium carbonate.
Therefore, the number of moles of potassium carbonate is equal to the number of moles of carbon dioxide.
Step 3: Calculate the percentage of potassium carbonate in the mixture.
To find the percentage of potassium carbonate in the mixture, we need to divide the moles of potassium carbonate by the total moles in the mixture and multiply by 100.
Now, we need information on the molar masses of the compounds involved in the reaction: potassium hydroxide (KOH) has a molar mass of 56.11 g/mol, potassium carbonate (K2CO3) has a molar mass of 138.21 g/mol, and potassium chloride (KCl) has a molar mass of 74.55 g/mol.
With this information, we can calculate the mass of potassium carbonate in the mixture and finally the percentage.
Let's plug in the values into the equations:
n = (740.0 torr * 0.249 L) / (0.08206 L·atm/(K·mol) * 295.15 K)
n = 8.72 * 10^-3 mol (approx.)
Percentage of potassium carbonate = (moles of K2CO3 / total moles) * 100%
Percentage of potassium carbonate = (8.72 * 10^-3 mol / total moles) * 100%
To find the percentage of potassium carbonate in the mixture, we need to determine the moles of carbon dioxide produced from the reaction and then use this information to calculate the moles of potassium carbonate.
Let's break down the steps to find the solution:
Step 1: Find the moles of carbon dioxide produced
Given:
- Volume of carbon dioxide gas = 249.0 mL
- Temperature of carbon dioxide gas = 22.0 °C
- Pressure of carbon dioxide gas = 740.0 torr
First, let's convert the volume of carbon dioxide gas from mL to L:
Volume = 249.0 mL × (1 L / 1000 mL) = 0.249 L
Next, convert the pressure from torr to atm:
Pressure = 740.0 torr × (1 atm / 760 torr) ≈ 0.974 atm
Now, we can find the moles of carbon dioxide using the ideal gas law equation:
PV = nRT
Where:
P = Pressure (in atm)
V = Volume (in L)
n = moles of gas
R = ideal gas constant (0.0821 L·atm/K·mol)
T = Temperature (in Kelvin)
Rearranging the equation:
n = (PV) / (RT)
Convert the temperature from Celsius to Kelvin:
Temperature = (22.0 °C + 273.15) K = 295.15 K
Substituting the values into the equation:
n = (0.974 atm × 0.249 L) / (0.0821 L·atm/K·mol × 295.15 K) ≈ 0.0100 mol
Therefore, approximately 0.0100 moles of carbon dioxide gas were produced.
Step 2: Calculate the moles of potassium carbonate
From the balanced chemical equation between potassium carbonate (K2CO3) and hydrochloric acid (HCl), we know that 1 mole of K2CO3 reacts with 2 moles of HCl to produce 1 mole of CO2 gas.
Therefore, the moles of potassium carbonate can be calculated using the mole ratio:
moles of K2CO3 = (moles of CO2) / 1 × 2
Substituting the value:
moles of K2CO3 = 0.0100 mol / 1 × 2 = 0.0200 mol
Step 3: Calculate the mass of potassium carbonate
The molar mass of potassium carbonate (K2CO3) is calculated as follows:
Molar mass of K2CO3 = (2 × Molar mass of K) + Molar mass of C + (3 × Molar mass of O)
Given:
Molar mass of K = 39.10 g/mol
Molar mass of C = 12.01 g/mol
Molar mass of O = 16.00 g/mol
Substituting the values:
Molar mass of K2CO3 = (2 × 39.10 g/mol) + 12.01 g/mol + (3 × 16.00 g/mol) ≈ 138.21 g/mol
Now we can calculate the mass of potassium carbonate:
mass of K2CO3 = moles of K2CO3 × Molar mass of K2CO3
mass of K2CO3 = 0.0200 mol × 138.21 g/mol ≈ 2.76 g
Step 4: Calculate the percentage of potassium carbonate
Finally, we can calculate the percentage of potassium carbonate in the mixture:
percentage of K2CO3 = (mass of K2CO3 / mass of mixture) × 100
Given:
mass of mixture = 5.000 g
Substituting the values:
percentage of K2CO3 = (2.76 g / 5.000 g) × 100 ≈ 55.2%
Therefore, the percentage of potassium carbonate in the mixture is approximately 55.2%.