A 1.60 g calcium supplement contains 37.8% Ca by mass. The calcium is present in the supplement as CaCO3. How many grams of CaCO3 are in the calcium supplement?

Answer 1

We are told the supplement is 1.6 g in total, and 37.8% of this supplement is calcium by weight. All calcium in the supplement is in the form of CaCO3 (molar mass=100.07 g).

1.6 (0.378) = 0.605 g of Ca

For every 1 mole of CaCO3 (molar mass of 100.07) there is 40.07 g of Ca.

If we use this proportion along with the amount in grams we know we have of calcium (0.605 g), we can determine the grams of CaCO3.

40.07/100.07 = 0.605/X

X=1.51 g of CaCO3

Answer 2

Broadly speaking, here are the steps to solving this problem:

Step 1: Calculate how much calcium is in the compounds

Step 2: Calculate what percent by mass calcium is in CaCO₃

Step 3: Calculate how much CaCO₃ you would need to provide the calcium

Let's get into the steps more concretely now!

Step 1:

We are told that 37.8% of the compound is Calcium. Since we have 1.60g of the compound, we can simply use the following equation to calculate the amount of calcium: Ca = 37.8%·1.60g = 0.6048g

Step 2:

To calculate the percent-by-mass of Calcium in CaCO₃, we simply divide the molar mass of Ca by the molar mass of CaCO₃. Looking at a periodic table, here are some useful molar masses:

1. Ca -- 40.078 g/mol
2. C -- 12.011 g/mol
3. O -- 15.999 g/mol

Thus, the molar mass of CaCO₃ is 40.078 + 12.011 + 15.999*3 = 100.086 g/mol. We divide the molar mass of Ca (40.078) by this to get the percent by mass of Calcium in CaCO₃. 40.078/100.086 = 40.04%.

Step 3:

Since we know how much calcium we need, and how much Calcium CaCO₃ provides, we can solve for our answer! We need 0.6048g of Calcium, and each gram of CaCO₃ provides 0.4004g of Calcium. To solve for the grams of CaCO₃, we simply divide 0.6048 ÷ 0.4004 = 1.5104g of CaCO₃. Now, our problem only had 3 significant figures, so we round answer down to 1.51g of CaCO_3.