You have a 0.5 M HEPES pH 7, and a 0.5 M HEPES pH 8 solution. How much of each stock solution do you need to make 125mL of a 50 mM HEPES pH 7.5 solution? How much water?
To calculate the amounts of the two stock solutions and the amount of water needed, we can use the formula:
(C1)(V1) + (C2)(V2) = (C3)(V3)
Where:
C1 = concentration of the first stock solution (0.5 M)
V1 = volume of the first stock solution used
C2 = concentration of the second stock solution (0.5 M)
V2 = volume of the second stock solution used
C3 = desired concentration of the final solution (50 mM or 0.05 M)
V3 = desired volume of the final solution (125 mL)
First, let's convert the desired concentration of the final solution from mM to M:
0.05 M = 0.050 L
Now, let's plug the values into the formula and solve for the volumes of the stock solutions and water:
(0.5 M)(V1) + (0.5 M)(V2) = (0.050 L)(125 mL)
Simplifying the equation:
0.5 V1 + 0.5 V2 = 0.050 L * 125 mL
Now, let's rearrange the equation to solve for V1:
V1 = (0.050 L * 125 mL - 0.5 V2) / 0.5
Now, let's substitute the desired pH values to find the volumes of the stock solutions:
For pH 7:
0.050 L * V1 = 125 mL * 7 / (7 - 7.5)
For pH 8:
0.050 L * V2 = 125 mL * 7 / (8 - 7.5)
Substituting the values:
V1 = 125 mL * 7 / (7 - 7.5)
V2 = 125 mL * 7 / (8 - 7.5)
Now, let's calculate the volumes of the stock solutions:
V1 = 125 mL * 7 / (7 - 7.5)
V2 = 125 mL * 7 / (8 - 7.5)
Simplifying the calculations:
V1 = 125 mL * 7 / (-0.5)
V2 = 125 mL * 7 / 0.5
Finally, let's calculate the volume of water:
Volume of water = V3 - (V1 + V2)
Substituting the values:
Volume of water = 125 mL - (V1 + V2)
After performing all the necessary calculations, the volumes of the stock solutions and water needed to make a 125 mL of a 50 mM HEPES pH 7.5 solution can be determined.