Potash is composed mainly of potassium carbonate, K2CO3. If 1.000g of potash reacts with sulfuric acid to produce 145 mL of carbon dioxide gas at STP, what is the percentage of potassium carbonate in the marble sample?
K2CO3 + H2SO4 ==> K2SO4 + H2O + CO2
145 mL x (1L/1000 mL) x (1 mole/22.4L) = ? moles CO2.
Convert moles CO2 to moles K2CO3 by
moles K2CO3 = moles CO2 x (1 mole K2CO3/1 mole CO2) = ?
grams CO2 = moles CO2 x molar mass CO2
%K2CO3 = (grams CO2/1.00 g sample) x 100 = ?
To find the percentage of potassium carbonate in the marble sample, we need to consider the molar ratio between potassium carbonate and carbon dioxide.
1. First, let's find the number of moles of carbon dioxide produced in the reaction. We know that 1 mole of any gas at STP occupies a volume of 22.4 liters. Since we have 145 mL of carbon dioxide, we can convert it to liters: 145 mL ÷ 1000 mL/L = 0.145 L.
2. Now, using the ideal gas law PV = nRT, we can calculate the number of moles (n) of carbon dioxide. At STP, the pressure (P) is 1 atm and the temperature (T) is 273.15 K. The gas constant (R) is 0.0821 L·atm/mol·K.
1 atm * 0.145 L = n * 0.0821 L·atm/mol·K * 273.15 K
n ≈ 0.00613 moles
3. From the balanced equation, we see that 1 mole of potassium carbonate produces 1 mole of carbon dioxide. Therefore, the number of moles of potassium carbonate in the reaction is also 0.00613.
4. Now, let's calculate the molar mass of potassium carbonate (K2CO3). The molar mass of potassium (K) is 39.10 g/mol, and the molar mass of carbon (C) is 12.01 g/mol. The molar mass of oxygen (O) is 16.00 g/mol.
Molar mass of K2CO3 = (2 * 39.10 g/mol) + 12.01 g/mol + (3 * 16.00 g/mol) ≈ 138.21 g/mol
5. Finally, to find the percentage of potassium carbonate in the marble sample, we can use the following formula:
Percentage of K2CO3 = (moles of K2CO3 * molar mass of K2CO3) / mass of the sample * 100
Assuming the 1.000g given is the mass of the sample:
Percentage of K2CO3 = (0.00613 * 138.21 g/mol) / 1.000 g * 100 ≈ 0.848%
Therefore, the percentage of potassium carbonate in the marble sample is approximately 0.848%.