In basic chemistry calculations, what is the gram formula mass (molar mass) of potassium carbonate, K2CO3, expressed in grams per mole?

Introduction / Context:
Questions about gram formula mass, also called molar mass, are very common in chemistry because they are the starting point for most stoichiometric calculations. Knowing how to calculate the gram formula mass of a compound like potassium carbonate, K2CO3, is essential for converting between moles and grams and for balancing reactions quantitatively. This question checks whether you can correctly use atomic masses from the periodic table to obtain the molar mass in grams per mole.

Given Data / Assumptions:

• Compound given: potassium carbonate, formula K2CO3.
• Approximate atomic masses used for calculation:
  • Potassium, K, has atomic mass about 39 g per mole.
  • Carbon, C, has atomic mass about 12 g per mole.
  • Oxygen, O, has atomic mass about 16 g per mole.
• We assume standard average atomic masses from the periodic table.

Concept / Approach:
The gram formula mass or molar mass of a compound is found by adding the atomic masses of all atoms present in its chemical formula. For K2CO3, the formula shows two potassium atoms, one carbon atom, and three oxygen atoms. The basic steps are to multiply each atomic mass by the number of atoms of that element in the formula, and then add all contributions. The final result will be in grams per mole and should match one of the given options.

Step-by-Step Solution:
Step 1: Write the formula K2CO3 and identify atom counts: 2 K atoms, 1 C atom, and 3 O atoms. Step 2: Use approximate atomic masses: K = 39 g per mole, C = 12 g per mole, O = 16 g per mole. Step 3: Calculate the total mass from potassium: 2 * 39 = 78 g per mole. Step 4: Calculate the contribution from carbon: 1 * 12 = 12 g per mole. Step 5: Calculate the contribution from oxygen: 3 * 16 = 48 g per mole. Step 6: Add the three contributions: 78 + 12 + 48 = 138 g per mole. Step 7: Compare 138 with the options and select 138 as the gram formula mass of K2CO3.

Verification / Alternative check:
As a quick check, you can estimate the range of the molar mass. Potassium carbonate contains two relatively heavy potassium atoms, so the total must be clearly above 100 g per mole. Adding two potassium atoms alone gives about 78 g per mole, and with one carbon and three oxygens added, the total should be somewhere between 130 and 150 g per mole. The exact calculation gives 138, which falls into this expected range and matches one of the answer choices, providing confidence in the result.

Why Other Options Are Wrong:
Option A, 147, is higher than the correct value and could come from incorrectly using a larger atomic mass for potassium or oxygen. Option C, 129, is lower than the correct mass and may arise if one of the element contributions is omitted. Option D, 116, is much too low for a compound containing two heavy potassium atoms and clearly does not match the correct summation of atomic masses. None of these incorrect values match the precise stepwise calculation for K2CO3.

Common Pitfalls:
Students often forget to multiply the atomic mass of an element by the number of atoms in the formula, especially for elements like potassium in K2CO3 that appear with a subscript. Another common error is to misread atomic masses from the periodic table or to confuse the formula of potassium carbonate with other similar compounds like potassium bicarbonate. Careful reading of the formula and systematic multiplication and addition are key to avoiding such mistakes. When uncertain, always recheck the counting of atoms and the arithmetic.

Final Answer:
The gram formula mass of potassium carbonate, K2CO3, is 138 g per mole.