To calculate the molarity (concentration in mol/dm³) of the solution produced when 10 cm³ of concentrated hydrochloric acid (HCl) is diluted to 1 dm³, we can follow these steps.
Step 1: Understand the given values
- Concentration of hydrochloric acid: 36% w/v
- Density of the hydrochloric acid: 1.18 g/cm³
- Volume of concentrated hydrochloric acid used: 10 cm³
- Final volume of the solution: 1 dm³ (1000 cm³)
Step 2: Calculate the mass of HCl in 10 cm³ of solution
Using the density, we find the mass of the 10 cm³ of concentrated acid:
\[ \text{Mass} = \text{Volume} \times \text{Density} = 10 , \text{cm}^3 \times 1.18 , \text{g/cm}^3 = 11.8 , \text{g} \]
Step 3: Calculate the mass of HCl in this solution
Since the solution is 36% w/v (meaning 36 grams of HCl per 100 cm³ of solution), we can find the amount of HCl in the 10 cm³ we have:
\[ \text{Mass of HCl} = \left( \frac{36 , \text{g HCl}}{100 , \text{cm}^3} \right) \times 10 , \text{cm}^3 = 3.6 , \text{g HCl} \]
Step 4: Convert grams of HCl to moles
To convert grams of HCl to moles, we use the molar mass of HCl, which is approximately 36.46 g/mol:
\[ \text{Moles of HCl} = \frac{\text{Mass of HCl}}{\text{Molar mass of HCl}} = \frac{3.6 , \text{g}}{36.46 , \text{g/mol}} \approx 0.0987 , \text{mol} \]
Step 5: Calculate the concentration of HCl in the final solution
Now we can find the concentration of HCl in the final 1 dm³ (1000 cm³) solution:
\[ \text{Concentration} = \frac{\text{Moles of HCl}}{\text{Volume of solution in dm³}} = \frac{0.0987 , \text{mol}}{1 , \text{dm}^3} = 0.0987 , \text{mol/dm}^3 \]
Summary of Concentration Calculation
The concentration of HCl in the final solution is approximately:
\[ \text{Concentration} \approx 0.0987 , \text{mol/dm}^3 \]
Step 6: Calculation for 5 cm³ concentration in mol/dm³
If instead we were to use 5 cm³ of concentrated hydrochloric acid, we would repeat the process:
- Calculate the mass of the HCl in 5 cm³:
\[ \text{Mass of HCl} = \left( \frac{36 , \text{g HCl}}{100 , \text{cm}^3} \right) \times 5 , \text{cm}^3 = 1.8 , \text{g HCl} \]
- Convert grams of HCl to moles:
\[ \text{Moles of HCl} = \frac{1.8 , \text{g}}{36.46 , \text{g/mol}} \approx 0.0494 , \text{mol} \]
- The concentration in 1 dm³ (1000 cm³) of solution:
\[ \text{Concentration} = \frac{0.0494 , \text{mol}}{1 , \text{dm}^3} = 0.0494 , \text{mol/dm}^3 \]
Summary of 5 cm³ Concentration Calculation
The concentration of HCl when 5 cm³ of concentrated acid is diluted to 1 dm³ is approximately:
\[ \text{Concentration} \approx 0.0494 , \text{mol/dm}^3 \]