How many grams of NaC2H3O2 (M = 82.034 g mol-1) should be dissolved in 400.0 g of water to prepare a solution which is 11.28 % NaC2H3O2 by mass?

Solve this equation for X:

X / (400 + X) = 0.1128

400 + X is the total number of grams in the resulting mixture. You do not need to use the number of grams per mole.

50.86

To calculate the number of grams of NaC2H3O2 needed to prepare a solution that is 11.28% NaC2H3O2 by mass, we'll follow these steps:

Step 1: Determine the mass of NaC2H3O2 in the final solution.
Step 2: Calculate the mass of the solution.
Step 3: Convert the mass of NaC2H3O2 to grams.

Let's start with step 1:

Step 1: Determine the mass of NaC2H3O2 in the final solution.

To find the mass of NaC2H3O2 in the final solution, we'll use the equation:

Mass of NaC2H3O2 = Mass of solution x Percentage of NaC2H3O2

Plugging in the given values:

Mass of NaC2H3O2 = 400.0 g x 11.28% = 45.12 g

Step 2: Calculate the mass of the solution.

The mass of the solution is the sum of the mass of water and the mass of NaC2H3O2:

Mass of solution = Mass of water + Mass of NaC2H3O2

Mass of solution = 400.0 g + 45.12 g = 445.12 g

Step 3: Convert the mass of NaC2H3O2 to grams.

Since the molar mass of NaC2H3O2 is given as 82.034 g/mol, we can calculate the number of moles of NaC2H3O2 as follows:

Moles of NaC2H3O2 = Mass of NaC2H3O2 / Molar mass of NaC2H3O2

Moles of NaC2H3O2 = 45.12 g / 82.034 g/mol ≈ 0.5498 moles

To convert moles to grams, we'll use the equation:

Grams of NaC2H3O2 = Moles of NaC2H3O2 x Molar mass of NaC2H3O2

Grams of NaC2H3O2 = 0.5498 moles x 82.034 g/mol ≈ 45.08 g

Therefore, approximately 45.08 grams of NaC2H3O2 should be dissolved in 400.0 grams of water to prepare a solution that is 11.28% NaC2H3O2 by mass.

To determine the number of grams needed to prepare a solution with a given percentage by mass, you can follow these steps:

1. Identify the given data:
- Mass of water = 400.0 g
- Percentage of NaC2H3O2 in the solution = 11.28%

2. Calculate the mass of NaC2H3O2 required:
- Mass of NaC2H3O2 = (Percentage of NaC2H3O2 / 100) x Mass of solution
- Mass of NaC2H3O2 = (11.28 / 100) x 400.0 g
- Mass of NaC2H3O2 = 45.12 g

3. Determine the number of moles of NaC2H3O2:
- Moles of NaC2H3O2 = Mass of NaC2H3O2 / Molar mass of NaC2H3O2
- Moles of NaC2H3O2 = 45.12 g / 82.034 g mol-1
- Moles of NaC2H3O2 ≈ 0.5497 mol

4. Calculate the mass of NaC2H3O2 needed:
- Mass of NaC2H3O2 needed = Moles of NaC2H3O2 x Molar mass of NaC2H3O2
- Mass of NaC2H3O2 needed = 0.5497 mol x 82.034 g mol-1
- Mass of NaC2H3O2 needed ≈ 45.06 g

Therefore, approximately 45.06 grams of NaC2H3O2 should be dissolved in 400.0 grams of water to prepare a solution that is 11.28% NaC2H3O2 by mass.