Problem 47 - Chemistry for Allied Health

Question

Calculate the moles of each of the following samples. a. \(25.0 \mathrm{~g} \mathrm{CO}_{2}\) b. \(10.0 \mathrm{~g} \mathrm{~N}_{2} \mathrm{H}_{4}\) c. \(85.0 \mathrm{~g} \mathrm{CaF}_{2}\) d. \(15.5 \mathrm{~g} \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) e. \(20.0 \mathrm{~g} \mathrm{CH}_{4}\) f. \(100.0 \mathrm{~g} \mathrm{C}_{6} \mathrm{H}_{6}\) g. \(30.0 \mathrm{~g} \mathrm{Na}_{2} \mathrm{SO}_{4}\) h. \(75.0 \mathrm{~g} \mathrm{~K}_{3} \mathrm{PO}_{4}\) i. \(50.0 \mathrm{~g} \mathrm{Al}\left(\mathrm{NO}_{3}\right)_{3}\) j. \(47.2 \mathrm{~g} \mathrm{Mg}_{3}\left(\mathrm{PO}_{4}\right)_{2}\)

Step-by-Step Solution

Answer

a) 0.568, b) 0.312, c) 1.088, d) 0.086, e) 1.247, f) 1.281, g) 0.211, h) 0.353, i) 0.235, j) 0.18 moles.

Step 1: Understand the Formula

To find the number of moles, use the formula: \( ext{Number of moles} = \frac{ ext{mass (g)}}{ ext{molar mass (g/mol)}} \). This formula relates mass to moles using molar mass.

Step 2: Calculate Moles of CO2

First, calculate the molar mass of CO2. The molar mass is obtained by adding 12.01 g/mol for carbon and 2 × 16.00 g/mol for oxygen, totaling 44.01 g/mol. So for 25.0 g of CO2, the moles are \( \frac{25.0}{44.01} \approx 0.568 \) moles of CO2.

Step 3: Calculate Moles of N2H4

Calculate the molar mass of N2H4: (2 × 14.01) + (4 × 1.01) = 32.06 g/mol. For 10.0 g, \( \frac{10.0}{32.06} \approx 0.312 \) moles of N2H4.

Step 4: Calculate Moles of CaF2

Molar mass calculation for CaF2: 40.08 (Ca) + (2 × 18.998) = 78.076 g/mol. For 85.0 g, \( \frac{85.0}{78.076} \approx 1.088 \) moles of CaF2.

Step 5: Calculate Moles of C6H12O6

Calculate molar mass of C6H12O6: (6 × 12.01) + (12 × 1.01) + (6 × 16.00) = 180.16 g/mol. For 15.5 g, \( \frac{15.5}{180.16} \approx 0.0860 \) moles of C6H12O6.

Step 6: Calculate Moles of CH4

Molar mass of CH4: 12.01 + (4 × 1.01) = 16.05 g/mol. For 20.0 g, \( \frac{20.0}{16.05} \approx 1.247 \) moles of CH4.

Step 7: Calculate Moles of C6H6

Calculate C6H6's molar mass: (6 × 12.01) + (6 × 1.01) = 78.11 g/mol. For 100.0 g, \( \frac{100.0}{78.11} \approx 1.281 \) moles of C6H6.

Step 8: Calculate Moles of Na2SO4

Molar mass of Na2SO4: (2 × 22.99) + 32.07 + (4 × 16.00) = 142.05 g/mol. For 30.0 g, \( \frac{30.0}{142.05} \approx 0.211 \) moles of Na2SO4.

Step 9: Calculate Moles of K3PO4

Calculate molar mass of K3PO4: (3 × 39.10) + 30.97 + (4 × 16.00) = 212.27 g/mol. For 75.0 g, \( \frac{75.0}{212.27} \approx 0.353 \) moles of K3PO4.

Step 10: Calculate Moles of Al(NO3)3

Molar mass for Al(NO3)3: 26.98 + (3 × [(14.01 + (3 × 16.00))]) = 213.01 g/mol. For 50.0 g, \( \frac{50.0}{213.01} \approx 0.235 \) moles of Al(NO3)3.

Step 11: Calculate Moles of Mg3(PO4)2

Calculate molar mass of Mg3(PO4)2: (3 × 24.305) + 2 × (30.97 + (4 × 16.00)) = 262.86 g/mol. For 47.2 g, \( \frac{47.2}{262.86} \approx 0.18 \) moles of Mg3(PO4)2.

Key Concepts

Molar Mass

In chemistry, molar mass is a crucial concept that helps us connect the mass of a substance to the quantity of atoms or molecules within it. Molar mass is defined as the mass of one mole of a substance and is usually expressed in grams per mole (g/mol). To compute the molar mass of any compound, sum up the atomic masses of all the atoms in its chemical formula. For example, water (H₂O) has a molar mass of 18.02 g/mol, calculated by adding the atomic masses of 2 hydrogen atoms (2 x 1.01 g/mol) and 1 oxygen atom (16.00 g/mol). Knowing the molar mass is essential in stoichiometry as it allows for converting between mass and moles, which is an integral part of solving many chemistry problems.

Moles of CO2

Carbon dioxide (CO₂) is a common compound that consists of one carbon atom and two oxygen atoms. To find the number of moles, you need the mass of the sample and its molar mass. First, calculate the molar mass of CO₂ by adding the atomic mass of carbon (12.01 g/mol) and oxygen (16.00 g/mol) twice: 12.01 + (2 x 16.00) = 44.01 g/mol. With a provided mass, such as 25.0 g of CO₂, you use the equation for moles: \[ \text{Moles of CO₂} = \frac{25.0}{44.01} \approx 0.568 \text{ moles} \].This simple division tells you how many moles are in that specific sample of CO₂.

Moles of N2H4

Hydrazine (N₂H₄) is an interesting compound composed of nitrogen and hydrogen. To determine moles, start by computing the molar mass. For hydrazine, add the molar mass of nitrogen (14.01 g/mol) times two and hydrogen (1.01 g/mol) times four: (2 x 14.01) + (4 x 1.01) = 32.06 g/mol. Knowing the mass, such as 10.0 g of hydrazine, allows you to calculate moles using:\[ \text{Moles of N₂H₄} = \frac{10.0}{32.06} \approx 0.312 \text{ moles} \].This shows how the mass-to-mole conversion can help in finding the right quantities for chemical reactions.

Moles of CaF2

Calcium fluoride (CaF₂) is a binary compound comprising calcium and fluorine. Calculating moles starts with finding the compound's molar mass. The molar mass of CaF₂ is evaluated by summing the molar mass of calcium (40.08 g/mol) and twice the molar mass of fluorine (18.998 g/mol): 40.08 + (2 x 18.998) = 78.076 g/mol. With 85.0 g of CaF₂, you can determine the moles using:\[ \text{Moles of CaF₂} = \frac{85.0}{78.076} \approx 1.088 \text{ moles} \].This calculation is key in many practical applications, such as in the field of materials science, where precise quantities are crucial.