George needs 50 liters of a solution that has a concentration of 30 g/ml for the manufacture of computer parts. George has an unlimited supply of a solution with a concentration of 39 g/ml. Using the Formula C1*V1=C2*V2 answer the following questions. Round answers to the nearest 10th. Use Unit Abbreviation Sheet for Units
How many liters of 39 g/ml equals the other mixture? How many liters of water must be added to this amount of the 39 g/ml solution to obtain the desired solution?
you are diluting it 39/30 times, or one part original, 9/30 part water
what is one part? 50/(39/30) or
1500/39=38.46 liters orig solution
water= 38.46*9/30=11.54 liters water.
Now for the other question, another way:
grams of stuff in 50 l: 50*30Kg/L
= 1500kg in 50 liters
grams of stuff in 38.46 liters of the original: 38.46*39kg/L=1499.94 rounded=1500g
Now round the two volumes to the nearest tenth
To answer these questions, we can use the formula C1*V1 = C2*V2, where C1 is the concentration of the initial solution, V1 is the volume of the initial solution, C2 is the concentration of the final solution, and V2 is the volume of the final solution.
1. How many liters of 39 g/ml equals the other mixture?
To find the volume of the 39 g/ml solution that is equivalent to 50 liters of the desired 30 g/ml solution, we can set up the equation as follows:
C1*V1 = C2*V2
39 g/ml * V1 = 30 g/ml * 50 liters
We can now solve for V1:
V1 = (30 g/ml * 50 liters) / 39 g/ml
V1 ≈ 38.5 liters
Therefore, approximately 38.5 liters of the 39 g/ml solution is equivalent to 50 liters of the desired 30 g/ml solution.
2. How many liters of water must be added to this amount of the 39 g/ml solution to obtain the desired solution?
To find the volume of water needed to be added to the 38.5 liters of the 39 g/ml solution to obtain the desired 30 g/ml solution, we can use the formula C1*V1 = C2*V2, where C1 is the concentration of water (0 g/ml), V1 is the volume of water to be added, C2 is the desired concentration (30 g/ml), and V2 is the final volume of the solution (V1 + 38.5 liters).
Setting up the equation:
C1*V1 = C2*V2
0 g/ml * V1 = 30 g/ml * (V1 + 38.5 liters)
We can now solve for V1:
0 g/ml * V1 = 30 g/ml * V1 + 30 g/ml * 38.5 liters
-30 g/ml * V1 = 30 g/ml * 38.5 liters
V1 = (30 g/ml * 38.5 liters) / -30 g/ml
V1 ≈ -38.5 liters
Since we cannot have a negative volume, the result is invalid. This means that no water needs to be added to the 38.5 liters of the 39 g/ml solution to obtain the desired 30 g/ml solution.