For statements 1 and 2, state for each if they are true or false. 1) A 1.0-gram sample of potassium sulfate K₂SO₄, molar mass 174.3 grams per mole, contains less potassium than a 1.0-gram sample of potassium citrate K₃C₆H₅O₇, molar mass 306.4 grams per mole. 2) There are more K atoms in 1.0 moles of potassium sulfate than in 1.0 moles of potassium citrate. If both are true, state if 2 is a correct explanation for 1.
We have two statements that refer to the salt potassium sulfate and potassium citrate. In the first statement, we’re comparing the amount of potassium in equivalent masses of these two salts. And in the second statement, we’re comparing the amount of potassium atoms in equivalent amounts of these two salts. So, the first thing we’ll need to compare these two salts is the amount of potassium per unit formula.
In potassium sulfate, we have two units of potassium per unit of potassium sulfate, while in potassium citrate, we have three units of potassium per unit of potassium citrate. The amount of potassium that is in each unit formula arises from the charge on the anion. Sulfate has a charge of 2− and citrate has a charge of 3−. Now, we can start comparing the amounts of potassium in our samples. So, the first thing we do is take the mass of potassium sulfate and divide it by the molar mass, 174.3 grams per mole. I’m using X here to indicate the formula K₂SO₄.
And lastly, we convert to amount of potassium by multiplying by two moles of potassium per mole of potassium sulfate. This simplifies to a fraction that’s not easy to do in our heads. So, I’m going to leave it for the present and come back to it later.
We can work out the amount of potassium in one gram of potassium citrate by taking that mass and dividing by the molar mass, 306.4 grams per mole. Here, I’m using Y in place of the full formula for potassium citrate. We then convert to moles of potassium by multiplying by three moles of potassium per mole of potassium citrate. And this results in another awkward fraction. So, I’m not going to evaluate that immediately.
Statement 1 suggests that our sample of potassium sulfate will contain less potassium than our sample of potassium citrate. So, our job is to figure out which of these fractions represents a bigger amount. Well, we can approximate two over 174.3 to one over 87. And we can simplify three divided by 306.4 to one over 102. 102 is the bigger of the two denominators. Therefore, one divided by 102 is smaller than one divided by 87. Therefore, statement 1 is false. A 1.0-gram sample of potassium sulfate contains more potassium than a 1.0-gram sample of potassium citrate.
Now, we can move on to statement 2. Statement 2 refers to the amount of potassium atoms in one mole of each salt. We can easily calculate the amount of potassium atoms in 1.0 moles of potassium sulfate because we know we get two moles of potassium atoms per mole of potassium sulfate. And our answer is 2.0 moles of potassium atoms.
And we can do the same for potassium citrate. We simply take on one mole and multiply it by three moles of potassium per mole of potassium citrate, giving us 3.0 moles of potassium atoms. Three is most certainly bigger than two. Therefore, there are actually fewer potassium atoms in 1.0 moles of potassium sulfate than in 1.0 moles of potassium citrate. Since neither statement is true, we don’t need to address the last part of the question.