Chapter 9: Problem 109

(a) What is the molar mass of sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right) ?\) (b) What is the mass of \(1.25\) moles of sucrose? (c) How many sucrose molecules are in \(1.25\) moles? (d) How many hydrogen atoms are in \(1.25\) moles of sucrose? (e) What is the mass in grams of the hydrogen atoms in part (d)?

Short Answer

Expert verified

The molar mass of sucrose is \(342.30 \, g/mol\). The mass of 1.25 moles of sucrose is \(427.88 \, g\). There are \(7.53 \times 10^{23}\) sucrose molecules in 1.25 moles. There are \(1.66 \times 10^{25}\) hydrogen atoms in 1.25 moles of sucrose, and the mass of these hydrogen atoms is \(27.77 \, g\).

Step by step solution

We first need to find the molar mass of sucrose. To do that, we look up the molar mass of each element in a periodic table and multiply it by the number of atoms in the sucrose formula. Then, we add them up to find the total molar mass of sucrose. Carbon: \(12 \times 12.01 \, g/mol \) Hydrogen: \(22 \times 1.008 \, g/mol \) Oxygen: \(11 \times 16.00 \, g/mol \) Now, we add these up to find the total molar mass of sucrose: #Step 2: Add each element's molar mass#

\(M_{sucrose} = (12 \times 12.01) + (22 \times 1.008) + (11 \times 16.00) = 144.12 + 22.18 + 176.00 = 342.30 \, g/mol\) #Step 3: Calculate the mass of 1.25 moles of sucrose#

We know that there are 1.25 moles of sucrose and that the molar mass of sucrose is 342.30 g/mol. We can now calculate the mass of 1.25 moles of sucrose: Mass = (Moles) x (Molar mass) = \(1.25 \, moles \times 342.30 \, g/mol = 427.88 \, g\) #Step 4: Determine the number of sucrose molecules in 1.25 moles#

To find the number of sucrose molecules in 1.25 moles, we will use Avogadro's number, which is \(6.022 \times 10^{23}\) molecules/mole. Sucrose molecules = (Moles) x (Avogadro's number) = \(1.25 \, moles \times 6.022 \times 10^{23} \, molecules/mole = 7.53 \times 10^{23}\) sucrose molecules #Step 5: Calculate the number of hydrogen atoms in 1.25 moles of sucrose#

Since we know there are 22 hydrogen atoms in one sucrose molecule, we need to multiply this by the number of sucrose molecules in 1.25 moles: Hydrogen atoms = (No. of sucrose molecules) x (22 H atoms/sucrose molecule) = \(7.53 \times 10^{23} \, sucrose \, molecules \times 22 \, H \, atoms/sucrose \, molecule = 1.66 \times 10^{25} \, H \, atoms\). #Step 6: Determine the mass of the hydrogen atoms in part (d)#

From part (d), we know there are \(1.66 \times 10^{25}\) hydrogen atoms. We will now calculate the mass of these hydrogen atoms, using the molar mass of hydrogen. First, we need to find the moles of hydrogen atoms: Moles of hydrogen atoms = \( \frac{1.66 \times 10^{25} \, atoms}{6.022 \times 10^{23} \, atoms/mol} = 27.55 \, moles\). Now we will calculate the mass of these moles of hydrogen atoms: Mass of hydrogen atoms = (Moles) x (Molar mass) = \(27.55 \, moles \times 1.008 \, g/mol = 27.77 \, g\).