Example 1.1: Weight/Weight (w/w)
To make up 250 g of a 5% aqueous solution of hydro-chloric acid (using 12 M HCI), multiply the total amount by the percent expressed as a decimal. The 5% aqueous solution can be expressed as
5
5% =
= 0.050
100
(Eq. 1.19)
Therefore, the calculation becomes
0.050 X 250 g = 12.5 g of 12M HC (Eq. 1.20)
Another way of arriving at the answer is to set up a ratio so that
Desired solution concentration = Final
product of 12 M HCl
5
100
=
250
x =12.5
(Eq. 1.21)

In this example, the goal is to prepare 250 g of a 5% aqueous solution of hydrochloric acid (HCl) using a concentrated 12 M solution of HCl.

### Explanation:

1. **Percent weight/weight (% w/w)** means that 5% of the solution’s weight will be HCl, and the remaining 95% will be water.
2. To find how much HCl is needed in 250 g of the solution, we convert the 5% to a decimal form:
   \[
   5\% = \frac{5}{100} = 0.050
   \]
   This gives the decimal value of the concentration.
   
3. Multiply the total weight of the solution (250 g) by this concentration (0.050) to get the mass of HCl needed:
   \[
   0.050 \times 250 \, \text{g} = 12.5 \, \text{g of HCl}
   \]
   This is the amount of HCl (in grams) required to make the solution.

4. The same result can be obtained using a ratio approach:
   \[
   \frac{5}{100} = \frac{12.5}{250}
   \]
   Solving for the unknown (amount of HCl) gives:
   \[
   x = 12.5 \, \text{g of HCl}
   \]

### Summary:
- You need 12.5 g of HCl to make 250 g of a 5% w/w aqueous solution of HCl.
- This can be calculated either by multiplying or by using ratios.

Do you need more details on any part of the explanation or have any questions?

### Related Questions:
1. How do you convert molarity into grams for a given volume?
2. What is the difference between weight/weight and weight/volume percentages?
3. How can you dilute a 12 M HCl solution to a lower concentration?
4. How do you calculate the mass of a solute required for a given molarity?
5. What is the formula to convert percentage concentration into molarity?

### Tip:
Always double-check if the percentage is given by weight or by volume, as this can change the calculations significantly.

Example 1.1: Weight/Weight (w/w) To make up 250 g of a 5% aqueous solution of hydrochloric acid (using 12 M HCl), multiply the total amount by the percent expressed as a decimal. The 5% aqueous solution can be expressed as 5 5% = = 0.050 100 Therefore, the calculation becomes 0.050 X 250 g = 12.5 g of 12M HCl Another way of arriving at the answer is to set up a ratio so that Desired solution concentration = Final product of 12 M HCl 5 100 = 250 x =12.5

Learn how to calculate the amount of HCl needed to prepare 250 g of a 5% w/w aqueous solution. This problem covers key concepts such as percentage calculations, ratio methods, and solution concentration. Suitable for students in Grades 10-12.

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