# Percent By Weight Formula

The percent by weight formula gives the amount of solute present in a given amount of solution. It is another way to represent the concentration of a solute like molarity, morality, and normality. It provides us with the mass percentage of a solute in the solution. The mass of the solution is evaluated by taking the masses of both solute and solvent into consideration. The percent by weight is expressed in percentage, and its value increases or decreases with an increase or decrease in the mass of solute and vice-versa.

**Percent By Weight Formula**

The percent by weight is equal to the ratio of the solute to the mass of the solution multiplied by 100. When a solute is dissolved in a solvent, a solution is formed. The percent by weight takes the masses of both solute and solvent one by one with the mass of solution and gives their concentration values. Its value is always less than 100% as the mass of solute or solvent cannot be greater than the mass of their solution. It is a unitless quantity as it provides the ratio of masses.

P = (m / M) Ã— 100Where,

m is the mass of solute or solvent,

M is the mass of solution.

For example,

Consider the deionization reaction of sodium chloride (NaCl) with water.

NaCl + H

_{2}O â†’ Na^{+}+ Cl^{–}Suppose 2 g of NaCl is dissolved in 100 g of water to produce positive and negative ions. Here, the solute is NaCl and the solvent is water.

Mass of solute = 2 g

Mass of solvent = 100 g

Mass of solution = (2 + 100) g = 102 g

So, the percent weight of both solute and solvent is,

Percent weight of solute NaCl = (2/102) Ã— 100

= 100/51

= 1.96 %

Percent weight of solvent water = (100/102) Ã— 100

= 10000/102

= 98.04 %

### Sample Problems

**Problem 1: Calculate the percent weight of solute if 5 g of it is dissolved in a solvent of 90 g.**

**Solution:**

Mass of solute (m) = 5 g

Mass of solvent = 90 g

Mass of solution (M) = (5 + 90) g = 95 g

Using the formula we get,

P = (m / M) Ã— 100

= (5/95) Ã— 100

= 5.26 %

**Problem 2: Calculate the percent weight of solute if 7 g of it is dissolved in a solvent of 110 g.**

**Solution:**

Mass of solute (m) = 7 g

Mass of solvent = 110 g

Mass of solution (M) = (7 + 110) g = 117 g

Using the formula we get,

P = (m / M) Ã— 100

= (7/117) Ã— 100

= 5.98 %

**Problem 3: Calculate the percent weight of solvent if 10 g of solute is dissolved in a solvent of 120 g.**

**Solution:**

Mass of solute = 10 g

Mass of solvent (m) = 120 g

Mass of solution (M) = (10 + 120) g = 130 g

Using the formula we get,

P = (m / M) Ã— 100

= (120/130) Ã— 100

= 92.30 %

**Problem 4: Calculate the percent weight of solvent if 15 g of solute is dissolved in a solvent of 45 g.**

**Solution:**

Mass of solute = 15 g

Mass of solvent (m) = 45 g

Mass of solution (M) = (15 + 45) g = 60 g

Using the formula we get,

P = (m / M) Ã— 100

= (45/60) Ã— 100

= 75 %

**Problem 5: Calculate the percent weight of solvent if 25 g of solute is present in a solution of 80 g.**

**Solution:**

Mass of solute = 25 g

Mass of solution (M) = 80 g

Mass of solvent (m) = 80 – 25 = 65 g

Using the formula we get,

P = (m / M) Ã— 100

= (65/80) Ã— 100

= 81.25 %

**Problem 6: Calculate the percent weight of solvent if 30 g of solute is present in a solution of 85 g.**

**Solution:**

Mass of solute = 30 g

Mass of solution (M) = 85 g

Mass of solvent (m) = 85 – 30 = 55 g

Using the formula we get,

P = (m / M) Ã— 100

= (55/85) Ã— 100

= 64.70 %

**Problem 7: Calculate the percent weight of solute if 81 g of solvent is present in a solution of 110 g.**

**Solution:**

Mass of solvent = 81 g

Mass of solution (M) = 110 g

Mass of solute (m) = 110 – 81 = 29 g

Using the formula we get,

P = (m / M) Ã— 100

= (29/110) Ã— 100

= 26.36 %

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