### Video Transcript

What is the amount of K2CO3, in moles, present in a 6.9-gram sample of K2CO3? Relative atomic masses: C equals 12, O equals 16, and K equals 39. (A) 0.010 moles, (B) 0.050 moles, (C) 0.50 moles, (D) 1.0 moles, (E) 2.0 moles.

In this question, we’ve been given the mass of a sample of K2CO3 or potassium carbonate. And we’ve been asked to convert this mass into an amount of K2CO3 in moles. Since the molar mass of a chemical species is equal to its mass divided by the amount in moles, we should be able to find the amount of potassium carbonate in moles by dividing the mass of potassium carbonate by its molar mass. We were given the mass of potassium carbonate in the question. It’s 6.9 grams. But we’ll need to calculate the molar mass of potassium carbonate using the atomic masses that were given.

Starting with potassium, we have two potassium atoms in potassium carbonate, each with an atomic mass of 39 grams per mole. We have just one carbon with an atomic mass of 12 grams per mole. And we have three oxygens, each with an atomic mass of 16 grams per mole. If we add up all of these masses, we’ll find that the molar mass of potassium carbonate is 138 grams per mole. So now, we can plug that number in for the molar mass and solve for the amount of potassium carbonate that we have in our sample in moles. But 6.9 divided by 138 might not be so easy to do in our heads. But 138 divided by two gives us 69. In other words, 69 divided by 138 is equal to one-half, which we could equivalently express as a decimal, 0.5.

Now, this expression, 69 divided by 138, is 10 times greater than what we’re trying to solve, since 6.9 times 10 gives us 69. Which means that we can divide the answer that we came up with for 69 divided by 138 by 10 to find what 6.9 divided by 138 equals. So dividing 0.5 by 10 would give us 0.05 moles of potassium carbonate, which matches answer choice (B). So the amount of potassium carbonate present in 6.9 grams of potassium carbonate is 0.050 moles.