In the laboratory, a student adds 57.6 mL of water to 10.9 mL of a 0.755 M perchloric acid solution. What is the concentration of the diluted solution ?
.755 M * 10.9 / (10.9 + 57.6)
I know I'm being picky BUT that answer, while true in most instances in reality, technically it is true ONLY when the volumes are additive. In some cases they are not.
To find the concentration of the diluted solution, we need to use the formula:
C1V1 = C2V2
where C1 is the initial concentration, V1 is the initial volume, C2 is the final concentration, and V2 is the final volume.
Given:
C1 = 0.755 M (perchloric acid)
V1 = 10.9 mL (initial volume)
V2 = 10.9 mL + 57.6 mL = 68.5 mL (final volume)
Plugging these values into the formula, we have:
(0.755 M)(10.9 mL) = C2(68.5 mL)
Simplifying the equation, we find:
C2 = (0.755 M)(10.9 mL) / (68.5 mL)
C2 = 12.98895 / 68.5
C2 ≈ 0.190 M
Therefore, the concentration of the diluted solution is approximately 0.190 M.
To find the concentration of the diluted solution, we need to calculate the moles of perchloric acid and the volume of the diluted solution. Here's how you can calculate it step by step:
Step 1: Calculate the moles of perchloric acid.
To find the moles of perchloric acid in the 10.9 mL solution, we multiply the volume (in liters) by the concentration (in moles per liter).
Moles of perchloric acid = volume (in liters) × concentration (in moles per liter)
First, we need to convert the volume from milliliters (mL) to liters (L).
Volume = 10.9 mL = 10.9/1000 L = 0.0109 L
Now we can calculate the moles of perchloric acid.
Moles of perchloric acid = 0.0109 L × 0.755 M = 0.0082245 moles
Step 2: Calculate the volume of the diluted solution.
To find the volume of the diluted solution, we add the volume of water (57.6 mL) to the volume of the 10.9 mL perchloric acid solution.
Volume of diluted solution = volume of water + volume of perchloric acid
First, we need to convert the volumes from milliliters (mL) to liters (L).
Volume of water = 57.6 mL = 57.6/1000 L = 0.0576 L
Now we can calculate the volume of the diluted solution.
Volume of diluted solution = 0.0576 L + 0.0109 L = 0.0685 L
Step 3: Calculate the concentration of the diluted solution.
To find the concentration of the diluted solution, we divide the moles of perchloric acid by the volume of the diluted solution.
Concentration = moles/volume
Now we can calculate the concentration of the diluted solution.
Concentration = 0.0082245 moles / 0.0685 L = 0.1201 M
Therefore, the concentration of the diluted solution is approximately 0.1201 M.