What is the mass of 2.25 times 10 to the negative three moles of ammonium sulfate? Give your answer in grams and to three decimal places. The molar mass of hydrogen equals one gram per mole. The molar mass of nitrogen equals 14 grams per mole. The molar mass of oxygen equals 16 grams per mole. And the molar mass of sulfur equals 32 grams per mole.
To convert between a mass in grams and the amount of a substance in moles, we can use this formula, which tells us the mass in grams is equal to the amount of substance in moles times the molar mass of the substance. The problem gave us the amount of the substance in moles. So we just need to calculate the molar mass to solve the problem. We can do this using the provided data.
The substance in this question is ammonium sulfate, which is made of ammonium and sulfate ions. Since ammonium has a charge of one plus and sulfate has a charge of two minus, we need two ammonium ions for every one sulfate ion so that the compound is neutral overall. So ammonium sulfate has the chemical formula (NH4)2SO4.
Now that we know the formula, let’s calculate the molar mass of ammonium sulfate. Hydrogen has a molar mass of one gram per mole. There are four hydrogen atoms in one ammonium ion. And there are two ammonium ions in ammonium sulfate. So there are a total of eight hydrogen atoms in ammonium sulfate. Nitrogen’s molar mass is 14 grams per mole. There is one nitrogen atom in ammonium, so there are two nitrogen atoms total in ammonium sulfate. Oxygen has a molar mass of 16 grams per mole. There are four oxygen atoms in ammonium sulfate. Finally, sulfur has a molar mass of 32 grams per mole. There’s just one sulfur atom in ammonium sulfate. If we multiply and add everything up, we’ll find the molar mass of ammonium sulfate is 132 grams per mole.
Now that we have the molar mass, we can solve the problem. The amount of ammonium sulfate that was given in the problem is 2.25 times 10 to the negative three moles. The molar mass that we just calculated is 132 grams per mole. The units of moles cancel, and we get 0.297 grams as our final answer, which is already reported to three decimal places. So the mass of 2.25 times 10 to the negative three moles of ammonium sulfate is 0.297 grams.