How to Find the Molar Mass of an Unknown Carbonate?

To determine the molar mass of an unknown carbonate (MCO₃), you'll typically use experimental data, often from a reaction involving the carbonate. Here's a step-by-step approach:

1. React the Carbonate and Collect Data

First, react a known mass of your unknown carbonate (MCO₃) with an excess of acid (e.g., hydrochloric acid, HCl). The reaction will produce a salt, water, and carbon dioxide gas:

MCO₃(s) + 2HCl(aq) → MCl₂(aq) + H₂O(l) + CO₂(g)

Crucially, you need to measure something quantifiable related to this reaction. Common methods involve:

• Measuring the Volume of CO₂ Produced: Collect the CO₂ gas and measure its volume at a known temperature and pressure.
• Gravimetric Analysis (Mass Change): React the carbonate and capture the CO₂ evolved in a CO₂ absorbent, or measure the mass lost by the reaction system. This method is less common for carbonates.
• Titration: React a known amount of MCO₃ with excess acid, and then titrate the remaining acid with a standard base.

2. Calculate the Moles of CO₂ (or Reactant/Product Measured)

Depending on your experimental method, calculate the moles of CO₂ produced:

• If you measured the volume of CO₂: Use the Ideal Gas Law (PV = nRT) to calculate the moles of CO₂. Rearrange the equation to solve for n (moles): n = PV/RT, where P is pressure, V is volume, R is the ideal gas constant (0.0821 L atm / (mol K) or 8.314 J/(mol K), depending on units), and T is the temperature in Kelvin.
• If you used mass change or CO₂ absorption: Calculate the moles of CO₂ from the mass of CO₂, using CO₂'s molar mass (44.01 g/mol).
• If you used Titration: Calculate the moles of acid that reacted with the carbonate and use stoichiometry.

3. Determine the Moles of MCO₃

From the balanced chemical equation (MCO₃(s) + 2HCl(aq) → MCl₂(aq) + H₂O(l) + CO₂(g)), you know that 1 mole of MCO₃ produces 1 mole of CO₂. Therefore:

Moles of MCO₃ = Moles of CO₂

4. Calculate the Molar Mass of MCO₃

The molar mass is calculated by dividing the mass of the MCO₃ used by the number of moles of MCO₃ calculated in the previous step:

Molar Mass of MCO₃ = (Mass of MCO₃ in grams) / (Moles of MCO₃)

5. Determine the Identity of the Metal (Optional)

If you want to identify the metal (M), subtract the molar mass of the carbonate ion (CO₃^2-, approximately 60.01 g/mol) from the molar mass of MCO₃ you calculated.

Molar Mass of Metal (M) = Molar Mass of MCO₃ - 60.01 g/mol

Compare the resulting molar mass to the molar masses of known metals to identify the metal.

Example

Suppose you react 1.00 g of an unknown carbonate and collect 0.227 L of CO₂ at 298 K and 1 atm.

1. Moles of CO₂: n = PV/RT = (1 atm 0.227 L) / (0.0821 L atm / (mol K) 298 K) = 0.00927 mol CO₂
2. Moles of MCO₃: Moles of MCO₃ = 0.00927 mol
3. Molar Mass of MCO₃: Molar Mass = 1.00 g / 0.00927 mol = 107.8 g/mol
4. Molar Mass of Metal (M): Molar Mass of M = 107.8 g/mol - 60.01 g/mol = 47.79 g/mol.

Looking at the periodic table, Titanium (Ti) has an atomic mass around 47.87 g/mol. Therefore, the unknown carbonate could be Titanium(II) Carbonate.