A .1360 g sample of a mixture of magnesium and calcium carbonates when treated with HCL evolves 32.25 cm cubed of carbon dioxed measured dry at STP. Calculate the percent of magnesium carbonate in the mixutre.
I am going to show you how to do this problem using chemical factors to convert from one material to another. This isn't taught in classes anymore but it sure is convenient.
Let x = mass MgCO3
then y = mass CaCO3
===================
X + Y = 0.1360g
X(molar mass CO2/molar mass MgCO3) + Y(molar mass CO2/molar mass CaCO3) = (0.03225*44/22.4)
Solve the two equations simultaneously for X and Y (actually, X is all you need). Then %MgCO3 =(mass MgCO3/mass sample)*100 = ??
[Note: molar mass CO2/molar mass MgCO3 convert X(grams MgCO3) to grams CO2. Similarly, molar mass CO2/molar mass CaCO3 conerts Y(grams CaCO3) to grams CO2. Both of these are chemical factors. On the right hand side, the 32.25 cc converts to 0.03225L and that divided by 22.4 converts to moles CO2. That multiplied by 44 converts to grams CO2 so basically we have the equation 2 just grams CO2 in terms of X + grams CO2 in terms of Y = grams CO2 attained.
To calculate the percent of magnesium carbonate in the mixture, you need to determine the amount of carbon dioxide (CO2) evolved specifically from the magnesium carbonate and the total amount of CO2 evolved.
Here's the step-by-step process to get the answer:
1. Calculate the number of moles of CO2 evolved:
- The volume of CO2 is given as 32.25 cm^3 at STP.
- At STP, 1 mole of any gas occupies 22.4 L or 22,400 cm^3.
- Convert the volume of CO2 evolved to moles: 32.25 cm^3 * (1 mole / 22,400 cm^3) = [moles of CO2]
2. Write the balanced chemical equation:
Since HCl reacts with both magnesium carbonate and calcium carbonate, it is necessary to have the balanced equation to determine the stoichiometry:
MgCO3 + 2HCl -> MgCl2 + H2O + CO2
The molar ratio of MgCO3 to CO2 is 1:1.
3. Calculate the molecular weight of CO2:
The molecular weight of CO2 is 44.01 g/mol.
4. Calculate the number of moles of magnesium carbonate (MgCO3):
From the molecular weight of CO2, calculate the number of moles:
[moles of CO2] * (1 mole MgCO3 / 1 mole CO2) = [moles of MgCO3]
5. Calculate the mass of magnesium carbonate (MgCO3):
Multiply the number of moles of MgCO3 by the molar mass of MgCO3:
[moles of MgCO3] * (molar mass of MgCO3) = [mass of MgCO3]
6. Calculate the percent of magnesium carbonate in the mixture:
Use the given mass of the sample to calculate the percentage:
([mass of MgCO3] / mass of the sample) * 100 = percent of MgCO3 in the mixture
Plug in the values and perform the calculations to find the answer.