Video: Calculating the Molar Mass of Ca(NO₃)₂⋅4H₂O

Which of the following is the molar mass of Ca(NO₃)₂⋅4H₂O? [A] 164 g/mol [B] 174 g/mol [C] 204 g/mol [D] 236 g/mol [E] 516 g/mol

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Video Transcript

Which of the following is the molar mass of Ca(NO₃)₂⋅4H₂O? (A) 164 grams per mole, (B) 174 grams per mole, (C) 204 grams per mole, (D) 236 grams per mole, or (E) 516 grams per mole.

The chemical formula that we’re given in this question is for hydrated salt. Sometimes when salts crystallize from aqueous solutions, the ions retain some of the water molecules in their crystal structure, which results in a hydrated salt. For the hydrated salt in this question, we have four water molecules in the crystal structure for each unit of calcium nitrate.

We need to calculate the molar mass of our hydrated salt for this question, which we can do by using the periodic table. For simplicity, rounded masses will be okay here, since all of our answer choices are nice round numbers.

First, let’s find the molar mass for our one unit of calcium nitrate. Calcium has a molar mass of 40 grams per mole. And there’s just one of them in calcium nitrate. Nitrogen has a molar mass of 14 grams per mole. And there’s two of them in one unit of calcium nitrate, which gives us 28 grams per mole. Oxygen has a molar mass of 16 grams per mole. And there’s six of them in one unit of calcium nitrate, which gives us a total of 96 grams per mole. Adding all of that together, we find that the molar mass of calcium nitrate is 164 grams per mole.

Now, let’s find the molar mass of the water molecule. Hydrogen has a molar mass of one gram per mole. And there’s two of them in a water molecule. So, that’s two grams per mole total. Oxygen again has a molar mass of 16 grams per mole. And there’s just one of them in a water molecule. So, the molar mass of our water molecule is 18 grams per mole. Now, we can find the total molar mass for our hydrated salt, which will be the molar mass of one unit of calcium nitrate plus the molar mass of four water molecules.

The mass of one unit of calcium nitrate is 164 grams per mole. And the mass of four water molecules is 72 grams per mole. If we add these numbers together, we’ll get 236 grams per mole, which matches answer choice (D).

So, the molar mass of the hydrated salt of calcium nitrate with four water molecules is 236 grams per mole.

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