Indicate how to mix two of the first concentration 3.2 M hydrochloric acid solution and the second to 15% by weight and density 1.30Kg / L to obtain 2.5 L of hydrochloric acid solution in 4.2M concentration
To determine how much of each solution to mix, we need to calculate the volumes based on the desired concentration and the properties of the two solutions.
Let's assign the following variables:
- V1: Volume of the first solution (3.2 M HCl)
- V2: Volume of the second solution (15% by weight, density 1.30 Kg/L)
- C1: Concentration of the first solution (3.2 M)
- C2: Concentration of the desired solution (4.2 M)
- V_final: Total volume of the final solution (2.5 L)
We need to find the values for V1 and V2.
First, let's calculate the amount of solute (hydrochloric acid) in the second solution:
- Amount of solute in the second solution = weight of solution * concentration
- Weight of solution = volume * density
- Amount of solute in the second solution = volume * density * concentration
For the final solution, the total amount of solute should be equal to the sum of the amounts of solute in the two solutions being mixed:
- Amount of solute in the final solution = Amount of solute in the first solution + Amount of solute in the second solution
Since we are mixing two solutions with different concentrations, we can use a simple equation to find the volumes:
- V_final * C2 = V1 * C1 + V2 * C2
Now we can solve this equation for V1 and V2 to find out how much of each solution to mix.
1. Substituting the given values:
- 2.5 L * 4.2 M = V1 * 3.2 M + V2 * 4.2 M
2. Rearranging the equation:
- 10.5 L = 3.2 V1 + 4.2 V2
Now we need another equation to solve for V1 and V2. We can use the equation for the amount of solute in the final solution.
3. Amount of solute in the final solution = Amount of solute in the first solution + Amount of solute in the second solution
- (2.5 L) * (4.2 M) = V1 * (3.2 M) + V2 * (15% * density)
We know that the density of the second solution is 1.30 Kg/L. Convert the weight percent of the second solution to concentration by dividing it by the molar mass of HCl.
4. Molar mass of HCl = 1 g/mol + 35.45 g/mol = 36.45 g/mol
- 15% by weight = 0.15 * density / molar mass (in kg/L)
- (15/100 * 1.30 Kg/L) / 0.03645 Kg/mol = concentration of the second solution in M
Substituting this value into equation 3:
- (2.5 L) * (4.2 M) = V1 * (3.2 M) + V2 * (concentration M)
Now we have two equations:
- 10.5 L = 3.2 V1 + 4.2 V2
- (2.5 L) * (4.2 M) = V1 * (3.2 M) + V2 * (concentration M)
Using these two equations, you can solve for the values of V1 and V2.