Question

Calculate the molar mass of powered fruit drink mix, made from sucrose (C12H22O11).Using stoichiometry, determine the mass of powdered drink mix needed to make a 1.0 M solution of 100 mL. (Hint: Use molarity = QUOTE to find the moles of drink mix, then convert moles to grams using a mole conversion.)What mass of powdered drink mix is needed to make a 0.5 M solution of 100 mL?

Answer 1

To prepare a 1.0 M sucrose solution, 34.234 grams of sucrose are needed for 100 mL of water, while a 0.5 M solution requires 17.117 grams for the same volume.

Step-by-step explanation:

Calculating the Molar Mass of Sucrose

The molar mass of sucrose (C12H22O11) is calculated by adding the atomic masses of its constituent elements. The atomic masses (rounded to two decimal places) are: Carbon (C) = 12.01 g/mol, Hydrogen (H) = 1.01 g/mol, and Oxygen (O) = 16.00 g/mol. Thus, the molar mass of sucrose is (12 * 12.01 g/mol) + (22 * 1.01 g/mol) + (11 * 16.00 g/mol) = 342.34 g/mol.

Calculating the Mass of Powdered Drink Mix for a 1.0 M Solution

To prepare a 1.0 M solution of sucrose in 100 mL, we must first convert the volume to liters (0.1 L). Then, we use the molarity equation where molarity = moles/volume. Therefore, 1.0 M = X moles/0.1 L, giving us X = 0.1 moles of sucrose. Multiplying the moles by the molar mass of sucrose, we get 0.1 moles * 342.34 g/mol = 34.234 grams of sucrose.

Calculating the Mass of Powdered Drink Mix for a 0.5 M Solution

For a 0.5 M solution, follow the same steps but with the altered molarity. Thus, 0.5 M = X moles/0.1 L, X = 0.05 moles. We then multiply the number of moles by the molar mass to find the mass needed: 0.05 moles * 342.34 g/mol = 17.117 grams of sucrose.

Answer 2

The molar mass of sucrose is 342.3 g/mol. To make a 1.0 M solution of 100 mL, 34.23 g of sucrose is needed. For a 0.5 M solution of the same volume, 17.12 g of sucrose is required.

Step-by-step explanation:

To calculate the molar mass of sucrose (C12H22O11), we first need to find the atomic mass of each element in the compound and multiply it by the number of atoms of that element in the molecule. The molar mass of sucrose is calculated as follows:

• 12 C atoms × 12.01 g/mol = 144.12 g/mol
• 22 H atoms × 1.008 g/mol = 22.176 g/mol
• 11 O atoms × 16.00 g/mol = 176.00 g/mol

Adding these together gives us a molar mass for sucrose of 342.3 g/mol.

To prepare a 1.0 M solution of 100 mL, we use the formula molarity (M) = moles of solute / liters of solution. Here, we need 1.0 mole of sucrose for 1 liter of solution, but since we only need 100 mL (0.1 L), we calculate the moles needed as follows:

1.0 M × 0.1 L = 0.1 moles of sucrose

Then, convert moles to grams:

0.1 moles × 342.3 g/mol = 34.23 g of sucrose

For a 0.5 M solution of 100 mL, the calculation is similar:

0.5 M × 0.1 L = 0.05 moles of sucrose

We then convert the moles to grams:

0.05 moles × 342.3 g/mol = 17.12 g of sucrose

Thus, 17.12 g of powdered drink mix is needed to make a 0.5 M solution of 100 mL.