How much water must be evaporated from 32 ounces of a 7% salt solution to make a 8% salt solution? (Answer is in ounces)
.07*32 =ounces of salt = 2.24
so we have 29.76 ounces of water
so
2.24 = .08(water + salt)
2.24 = .08 (water + 2.24)
2.24 = .08 water + .18
2.06 = .08*water
water = 25.75
so
water removed = 29.76-25.75
about 4 oz
V = Volume of 7% salt solution = 32 ounces
s = Volume of salt in 7% salt solution
w = Volume of wather 7% salt solution
s = 7 % of 32 = ( 7 / 100 ) ∙ 32 =
0.07 ∙ 32 = 2.24 ounces
Volume of water in 7% salt solution:
w = 93 % of V =
93 % of 32 = ( 93 / 100 ) ∙ 32 =
0.93 ∙ 32 = 29.76 ounces
V1 = Volume of 8% salt solution
s1 = Volume of salt in 8% salt solution
w1 = Volume of wather 8% salt
In 8% salt solution 2.24 ounces of salt represent 8 % of volume
s1 = 2.24 ounces
s1 = 0.08 V1
2.24 = 0.08 V1
V1 = 2.24 / 0.08 = 28 ounces
92 % of this volume is wather.
w1 = 0.92 ∙ 28 = 25.76 ounces
∆w = w - w1 = 29.76 ounces - 25.76 ounces = 4 ounces
OR
∆V = V - V1 = 32 - 28 = 4 ounces
s / v = .07
s / (v - x) = .08
dividing ... (v - x) / v = 7 / 8
1 - x/v = 7/8 ... 1/8 = x/v ... x = v/8
To find out how much water needs to be evaporated from a salt solution to achieve a desired concentration, we need to follow these steps:
Step 1: Understand the problem.
We have a 32-ounce solution that contains 7% salt. We want to evaporate water from this solution to increase the salt concentration to 8%.
Step 2: Determine the initial amount of salt in the solution.
Since the solution is 7% salt, we can calculate the initial amount of salt in the solution as follows:
Initial salt amount = 7% × 32 ounces.
Step 3: Determine the desired amount of salt in the final solution.
To obtain an 8% salt solution, we need to calculate the amount of salt required in the final solution:
Desired salt amount = 8% × (32 ounces - x ounces), where x is the amount of water evaporated.
Step 4: Set up an equation.
We can set up an equation by equating the initial salt amount (step 2) to the desired salt amount (step 3):
7% × 32 ounces = 8% × (32 ounces - x ounces).
Step 5: Solve the equation.
Now we can solve for x, the amount of water that needs to be evaporated:
0.07 × 32 = 0.08 × (32 - x).
0.07 × 32 = 0.08 × 32 - 0.08x.
2.24 = 2.56 - 0.08x.
0.08x = 2.56 - 2.24.
0.08x = 0.32.
x = 0.32 / 0.08.
x = 4.
Therefore, 4 ounces of water needs to be evaporated from the 32-ounce solution to make an 8% salt solution.