a bottel contains 500 ml of 2.4 M HCL. How much water should be added to dilute it to 1.6 M HCL. Solution
To dilute the HCL solution from 2.4 M to 1.6 M, we need to add water to reduce the concentration of the acid. Here's how to calculate how much water you should add:
Step 1: Determine the initial number of moles of HCL in the original solution.
Given the initial concentration (C1) of HCL as 2.4 M and the volume (V1) as 500 ml, we can calculate the initial number of moles (n1) using the formula:
n1 = C1 * V1
n1 = 2.4 M * 500 ml
Make sure to convert milliliters to liters:
n1 = 2.4 M * (500 ml / 1000 ml/L)
n1 = 2.4 M * 0.5 L
Step 2: Determine the final number of moles of HCL required.
To achieve a final concentration (C2) of 1.6 M, we multiply the desired concentration by the total volume (V1 + V2).
n2 = C2 * (V1 + V2)
We substitute the known values:
n2 = 1.6 M * (500 ml + V2)
n2 = 1.6 M * (0.5 L + V2)
Step 3: Equate the initial and final moles of HCL.
Since the number of moles before and after dilution must be the same, we can set up an equation:
n1 = n2
2.4 M * 0.5 L = 1.6 M * (0.5 L + V2)
Step 4: Solve for V2 to find the amount of water to be added.
Now we can solve the equation for V2:
1.2 L = 0.8 L + 1.6 M * V2
0.4 L = 1.6 M * V2
Divide both sides by 1.6 M:
V2 = 0.4 L / 1.6 M
V2 = 0.25 L
So, you should add 0.25 liters (or 250 ml) of water to dilute the 500 ml of 2.4 M HCL solution to a 1.6 M HCL solution.
To dilute the 2.4 M HCL solution to 1.6 M HCL, you can use the formula for dilution:
C1V1 = C2V2
where:
C1 = initial concentration of the HCL solution (2.4 M)
V1 = initial volume of the HCL solution (500 ml)
C2 = final concentration of the HCL solution (1.6 M)
V2 = final volume of the HCL solution (500 ml + V_water)
In this case, we know the values for C1, V1, and C2, and we need to calculate V2 (the final volume of the HCL solution). Let's plug the values into the formula and solve for V2:
(2.4 M)(500 ml) = (1.6 M)(500 ml + V_water)
1200 ml = 800 ml + 1.6 M·V_water
Subtract 800 ml from both sides:
400 ml = 1.6 M·V_water
Now, divide both sides of the equation by 1.6 M:
V_water = 400 ml / 1.6 M
V_water = 250 ml
Therefore, you should add 250 ml of water to the bottle containing 500 ml of 2.4 M HCL to dilute it to a 1.6 M HCL solution.