Determine the volume, in milliliters, required to prepare each of the following diluted solutions.
40.0mL of a 2.75M KNO3 solution using a 1.00M KNO3 solution
45.0mL of a 2.90M H2SO4 solution using a 6.00M H2SO4 solution
0.700L of a 2.10M NH4Cl solution using a 5.00M NH4Cl solution
To determine the volume of the concentrated solution required to prepare each diluted solution, we can use the dilution formula:
C1V1 = C2V2
Where:
C1 = concentration of the concentrated solution
V1 = volume of the concentrated solution
C2 = concentration of the diluted solution
V2 = volume of the diluted solution (final volume)
Let's calculate the required volumes for each scenario step-by-step:
1. For 40.0 mL of a 2.75 M KNO3 solution using a 1.00 M KNO3 solution:
C1 = 1.00 M
V1 = ?
C2 = 2.75 M
V2 = 40.0 mL
Using the dilution formula:
C1V1 = C2V2
1.00 M * V1 = 2.75 M * 40.0 mL
V1 = (2.75 M * 40.0 mL) / 1.00 M
V1 = 110.0 mL
Therefore, you would need to measure 110.0 mL of the 1.00 M KNO3 solution.
2. For 45.0 mL of a 2.90 M H2SO4 solution using a 6.00 M H2SO4 solution:
C1 = 6.00 M
V1 = ?
C2 = 2.90 M
V2 = 45.0 mL
Using the dilution formula:
C1V1 = C2V2
6.00 M * V1 = 2.90 M * 45.0 mL
V1 = (2.90 M * 45.0 mL) / 6.00 M
V1 = 21.75 mL
Therefore, you would need to measure 21.75 mL of the 6.00 M H2SO4 solution.
3. For 0.700 L of a 2.10 M NH4Cl solution using a 5.00 M NH4Cl solution:
C1 = 5.00 M
V1 = ?
C2 = 2.10 M
V2 = 0.700 L
Note: We need to convert liters to milliliters since the concentration is given in milliliters.
Using the dilution formula:
C1V1 = C2V2
5.00 M * V1 = 2.10 M * 0.700 L * 1000 mL/L
V1 = (2.10 M * 0.700 L * 1000 mL/L) / 5.00 M
V1 = 294.0 mL
Therefore, you would need to measure 294.0 mL of the 5.00 M NH4Cl solution.
To determine the volume of a concentrated solution needed to prepare a diluted solution, we can use the formula for dilution:
McVc = MdVd
where Mc is the concentration of the concentrated solution, Vc is the volume of the concentrated solution, Md is the concentration of the diluted solution, and Vd is the volume of the diluted solution.
Let's solve the problems step by step.
1. For the first problem, we are given:
Mc = 2.75M
Md = 1.00M
Vd = 40.0mL
We need to find Vc.
Using the formula:
2.75M * Vc = 1.00M * 40.0mL
Rearranging the equation to solve for Vc:
Vc = (1.00M * 40.0mL) / 2.75M
Vc = 14.55mL
So, to prepare a 40.0mL diluted solution with a concentration of 2.75M using a 1.00M KNO3 solution, 14.55mL of the 1.00M KNO3 solution is required.
2. For the second problem, we are given:
Mc = 6.00M
Md = 2.90M
Vd = 45.0mL
We need to find Vc.
Using the formula:
6.00M * Vc = 2.90M * 45.0mL
Rearranging the equation to solve for Vc:
Vc = (2.90M * 45.0mL) / 6.00M
Vc = 21.75mL
So, to prepare a 45.0mL diluted solution with a concentration of 2.90M using a 6.00M H2SO4 solution, 21.75mL of the 6.00M H2SO4 solution is required.
3. For the third problem, we are given:
Mc = 5.00M
Md = 2.10M
Vd = 0.700L
We need to find Vc.
Using the formula:
5.00M * Vc = 2.10M * 0.700L
Rearranging the equation to solve for Vc:
Vc = (2.10M * 0.700L) / 5.00M
Vc = 0.294L
Converting liters to milliliters:
Vc = 0.294L * 1000mL/L
Vc = 294mL
So, to prepare a 0.700L diluted solution with a concentration of 2.10M using a 5.00M NH4Cl solution, 294mL of the 5.00M NH4Cl solution is required.