you are given one litre each of 0.5 M HCL and 0.2 M HCL. How should they be mixed so as to give maximum volume of 0.4 M HCL.
Solution
To determine the mixture that will yield the maximum volume of 0.4 M HCl, you can use the formula for dilution:
C1V1 = C2V2
where:
C1 = initial concentration (0.5 M or 0.2 M HCl)
V1 = initial volume (unknown)
C2 = final concentration (0.4 M HCl)
V2 = final volume (unknown, we want to maximize this)
Let's denote the volume of 0.5 M HCl as V_0.5 and the volume of 0.2 M HCl as V_0.2.
First, we can determine the ratio of the volumes of the solutions:
0.5V_0.5 + 0.2V_0.2 = 0.4(V_0.5 + V_0.2)
Now, let's solve this equation to find the ratio of V_0.5 to V_0.2:
0.5V_0.5 + 0.2V_0.2 = 0.4V_0.5 + 0.4V_0.2
0.1V_0.5 = 0.2V_0.2
V_0.5 = 2V_0.2
We can see that the volume of the 0.5 M HCl solution should be double the volume of the 0.2 M HCl solution to obtain the desired concentration.
Now, let's substitute this ratio back into the initial equation to find the specific volumes:
0.5(2V_0.2) + 0.2V_0.2 = 0.4(2V_0.2 + V_0.2)
1V_0.2 + 0.2V_0.2 = 0.6V_0.2
1.2V_0.2 = 0.6V_0.2
V_0.2 = 1L
Since the volume of the 0.2 M HCl solution is given as 1 litre, we can determine the volume of the 0.5 M HCl solution:
V_0.5 = 2V_0.2 = 2L
Therefore, to obtain the maximum volume of 0.4 M HCl, you should mix 2 liters of 0.5 M HCl solution with 1 liter of 0.2 M HCl solution.
To determine how to mix the given solutions to obtain the maximum volume of 0.4 M HCL, we can use the concept of the total moles of solute before and after mixing.
Let's start by calculating the number of moles of HCL in each solution:
For 0.5 M HCL:
Molarity (M) = Moles (mol) / Volume (L)
0.5 = Moles / 1
Moles = 0.5 mol
For 0.2 M HCL:
Molarity (M) = Moles (mol) / Volume (L)
0.2 = Moles / 1
Moles = 0.2 mol
Now, let's determine the total moles of HCL in the two solutions:
Total moles of HCL = Moles in 0.5 M HCL + Moles in 0.2 M HCL
Total moles of HCL = 0.5 mol + 0.2 mol
Total moles of HCL = 0.7 mol
Next, we need to find out the total volume of the resulting 0.4 M HCL solution. To do this, we'll use the equation:
Molarity (M) = Moles (mol) / Volume (L)
Rearranging the equation, we have:
Volume (L) = Moles (mol) / Molarity (M)
Volume (L) = 0.7 mol / 0.4 M
Volume (L) = 1.75 L
Therefore, to obtain the maximum volume of 0.4 M HCL, mix 0.5 L of 0.5 M HCL with 1.25 L of 0.2 M HCL.
Note that while mixing the solutions, the total moles of solute remain constant, and the final concentration is determined by the combined volumes of the solutions.