To determine the mass of magnesium carbonate in the mixture, we need to calculate the moles of magnesium carbonate first.
The molar mass of carbon dioxide (CO2) is approximately 44.01 g/mol. Given that 0.06464 moles of CO2 were produced, we can calculate the mass of CO2 as follows:
Mass of CO2 = moles of CO2 × molar mass of CO2 = 0.06464 moles × 44.01 g/mol ≈ 2.849 g
Now, let's assume that x grams of the mixture is composed of magnesium carbonate. Therefore, the remaining mass (6.0 g - x) will be the mass of calcium carbonate.
According to the balanced chemical equation for the decomposition of magnesium carbonate (MgCO3), one mole of MgCO3 produces one mole of CO2. Hence, the moles of CO2 produced will be equal to the moles of magnesium carbonate decomposed.
Given that the molar mass of magnesium carbonate (MgCO3) is approximately 84.32 g/mol, we can calculate the moles of magnesium carbonate as follows:
Moles of MgCO3 = Mass of CO2 ÷ molar mass of MgCO3 = 2.849 g ÷ 84.32 g/mol ≈ 0.0338 moles
Since the ratio of magnesium carbonate to the total mixture is 0.0338 moles / (0.0338 moles + 0.06464 moles), we can calculate the mass of magnesium carbonate as:
Mass of magnesium carbonate = x Mass of calcium carbonate = 6.0 g - x
0.0338 moles / (0.0338 moles + 0.06464 moles) = x / (x + (6.0 g - x))
0.0338 / 0.09844 = x / (6.0 - x)
0.343 = x / (6.0 - x)
0.343(6.0 - x) = x
2.058 - 0.343x = x
2.058 = 1.343x
x ≈ 2.058 / 1.343 x ≈ 1.534 g
Therefore, the mass of magnesium carbonate in the mixture is approximately 1.534 grams.