Three solutions
56.0 mL of 0.2 M KNO3;
57.0 mL of 0.6 M Ca(NO3)2; and 57.0 mL of 0.325 M KCl
were poured together to make one new solution. What is the concentration of Cl− after mixing?
mols = M x L
Only KCl has Cl^- so that has been diluted from 57.0 mL to 57.0+57.0 + 56.0 = 170 mL.
New concn is 0.325 x (56.0/170) = ?
Another way is to find mols Cl^-. That is M x L = 0.325 x 0.057L = ?
Then M KCl = mols KCl/L solution = (0.325*0.057)/(0.056+0.057+0.057)
To find the concentration of Cl− after mixing the three solutions, we need to calculate the total amount of Cl− ions in the final solution and then divide it by the total volume of the solution.
Step 1: Calculate the amount of Cl− ions in each solution.
For the first solution, 56.0 mL of 0.2 M KNO3:
The concentration of KNO3 is 0.2 M, so the concentration of Cl− ions is also 0.2 M.
For the second solution, 57.0 mL of 0.6 M Ca(NO3)2:
Since each Ca(NO3)2 molecule contains 2 Cl− ions, the concentration of Cl− ions is 0.6 M × 2 = 1.2 M.
For the third solution, 57.0 mL of 0.325 M KCl:
The concentration of KCl is 0.325 M, so the concentration of Cl− ions is also 0.325 M.
Step 2: Calculate the total amount of Cl− ions in the final solution.
The total amount of Cl− ions = (Concentration of Cl− ions in the first solution × Volume of the first solution) + (Concentration of Cl− ions in the second solution × Volume of the second solution) + (Concentration of Cl− ions in the third solution × Volume of the third solution)
= (0.2 M × 56.0 mL) + (1.2 M × 57.0 mL) + (0.325 M × 57.0 mL)
= 11.2 mmol + 68.4 mmol + 18.525 mmol
= 98.125 mmol
Step 3: Calculate the concentration of Cl− ions in the final solution.
The total volume of the final solution = Volume of the first solution + Volume of the second solution + Volume of the third solution
= 56.0 mL + 57.0 mL + 57.0 mL
= 170.0 mL
Concentration of Cl− ions in the final solution = Total amount of Cl− ions / Total volume of the final solution
= 98.125 mmol / 170.0 mL
= 0.577 molar or 0.577 M
Therefore, the concentration of Cl− ions in the final solution is 0.577 M.
To find the concentration of Cl− after mixing the solutions, we need to calculate the total moles of Cl− and the total volume of the final solution.
Let's start by calculating the moles of Cl− in each solution:
For the first solution, which is KNO3, we need to multiply the volume (56.0 mL) by the molarity (0.2 M) and the number of Cl− ions (1). This will give us the moles of Cl− in the KNO3 solution.
Moles of Cl− from KNO3 = volume (56.0 mL) × molarity (0.2 M) × number of Cl− ions (1)
For the second solution, which is Ca(NO3)2, we need to multiply the volume (57.0 mL) by the molarity (0.6 M) and the number of Cl− ions (2). This will give us the moles of Cl− in the Ca(NO3)2 solution.
Moles of Cl− from Ca(NO3)2 = volume (57.0 mL) × molarity (0.6 M) × number of Cl− ions (2)
And for the third solution, which is KCl, we need to multiply the volume (57.0 mL) by the molarity (0.325 M) and the number of Cl− ions (1). This will give us the moles of Cl− in the KCl solution.
Moles of Cl− from KCl = volume (57.0 mL) × molarity (0.325 M) × number of Cl− ions (1)
Now, we can add up the moles of Cl− from each solution to find the total moles of Cl−:
Total moles of Cl− = Moles of Cl− from KNO3 + Moles of Cl− from Ca(NO3)2 + Moles of Cl− from KCl
After finding the total moles of Cl−, we need to calculate the total volume of the final solution. We can do this by adding up the volumes of the three solutions:
Total volume of the final solution = Volume of the KNO3 solution + Volume of the Ca(NO3)2 solution + Volume of the KCl solution
Finally, we can calculate the concentration of Cl− in the final solution by dividing the total moles of Cl− by the total volume of the final solution:
Concentration of Cl− = Total moles of Cl− / Total volume of the final solution
By following these steps, you can find the concentration of Cl− after mixing the three solutions.