Question

(a) What is the mass, in grams, of \(2.50 \times 10^{-3}\) mol of ammonium phosphate? (b) How many moles of chloride ions are in \(0.2550 \mathrm{~g}\) of aluminum chloride? (c) What is the mass, in grams, of \(7.70 \times 10^{20}\) molecules of caffeine, \(\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{~N}_{4} \mathrm{O}_{2} ?\) (d) What is the molar mass of cholesterol if \(0.00105 \mathrm{~mol}\) weighs \(0.406 \mathrm{~g}\) ?

Short answer

(a) The mass of \(2.50 \times 10^{-3}\) mol of ammonium phosphate is 0.373 g. (b) There are \(5.73 \times 10^{-3}\) moles of chloride ions in 0.2550 g of aluminum chloride. (c) The mass of \(7.70 \times 10^{20}\) molecules of caffeine is 0.249 g. (d) The molar mass of cholesterol is 386.67 g/mol.

Step-by-step solution

(a) Find molar mass of Ammonium Phosphate

To find the mass, we first have to find the molar mass of ammonium phosphate, which has the formula (NH4)3PO4. The molar mass of N = 14.01 g/mol The molar mass of H = 1.01 g/mol The molar mass of P = 30.97 g/mol The molar mass of O = 16.00 g/mol The molar mass of ammonium phosphate is: \((3 * 14.01) + (12 * 1.01) + 30.97 + (4 * 16.00) = 149.09 \mathrm{~g/mol}\)

(a) Find mass

Now we can find the mass, by multiplying the given moles with the molar mass of ammonium phosphate. Mass = moles * molar mass Mass = \(2.50 \times 10^{-3}\) mol * 149.09 g/mol = 0.373 g

(b) Moles of Aluminum Chloride

First find the molar mass of aluminum chloride, AlCl3. The molar mass of Al = 26.98 g/mol The molar mass of Cl = 35.45 g/mol Molar mass of AlCl3 = 26.98 + (3 * 35.45) = 133.33 g/mol Now find the moles of aluminum chloride given the mass. Moles = mass / molar mass Moles = \(0.2550 \mathrm{~g} / 133.33 \mathrm{~g/mol}\) = \(1.91 \times 10^{-3}\) mol

(b) Moles of Chloride

In 1 mol of AlCl3, there are 3 moles of chloride ions (Cl-). Therefore, the moles of chloride ions in \(1.91 \times 10^{-3}\) mol of AlCl3 is: \((1.91 \times 10^{-3} \mathrm{~mol}) * 3 = 5.73 \times 10^{-3} \mathrm{~mol}\)

(c) Molar mass and moles of Caffeine

First, find the molar mass of caffeine, C8H10N4O2. Molar mass of C = 12.01 g/mol Molar mass of N = 14.01 g/mol Molar mass of O = 16.00 g/mol Molar mass of caffeine = \((8 * 12.01) + (10 * 1.01) + (4 * 14.01) + (2 * 16.00) = 194.19 \mathrm{~g/mol}\) Now, find the moles of caffeine from the given number of molecules, using Avogadro's number (\(6.022 \times 10^{23} \mathrm{~mol^{-1}}\)). Moles = number of molecules / Avogadro's number Moles = \(7.70 \times 10^{20}\) molecules / \(6.022 \times 10^{23} \mathrm{~mol^{-1}}\) = \(1.28 \times 10^{-3} \mathrm{~mol}\)

(c) Mass of Caffeine

Now, find the mass from the moles and molar mass of caffeine. Mass = moles * molar mass Mass = \(1.28 \times 10^{-3} \mathrm{~mol} * 194.19 \mathrm{~g/mol}\) = 0.249 g

(d) Molar Mass of Cholesterol

Use the provided mass and moles of cholesterol to find its molar mass. Molar mass = mass / moles Molar mass = \(0.406 \mathrm{~g} / 0.00105 \mathrm{~mol}\) = 386.67 g/mol