A pot contains 6 liters of brine at a concentration of 120g/l. How many liters of the water should be boiled off so that concentration of the brine is 200g/l.
let the amount boiled off be x L
amount of brine = 6 (120 g/L) = 720 g
that must stay constant
(6-x)(200 g/L) = 720 g
1200 - 200x = 720
-200x = -480
x = 2.4
2.4 L must be boiled off
check:
liquid left = 6-2.4 = 3.6 L
but there must still be 720 g in there
concentration = 720/3.6 = 200 g/L
To find out how many liters of water should be boiled off, we need to determine the initial mass of salt in the brine and the final volume of the brine.
Step 1: Calculate the initial mass of salt in the brine.
The initial concentration of the brine is 120g/l, and the initial volume is 6 liters. Therefore, the initial mass of salt in the brine is:
Mass = Concentration × Volume
Mass = 120g/l × 6 liters
Mass = 720 grams
Step 2: Determine the final volume of the brine.
The desired concentration of the brine is 200g/l. Let's assume the final volume of the brine after boiling off water is V liters.
Since the mass of salt remains constant, we can write the equation:
Initial Mass = Final Concentration × Final Volume
720 grams = 200g/l × V liters
Now, solve for V:
V liters = 720 grams / 200g/l
V liters = 3.6 liters
So, the final volume of the brine after boiling off water is 3.6 liters.
Step 3: Calculate the amount of water that needs to be boiled off.
To find the amount of water that needs to be boiled off, subtract the final volume of the brine from the initial volume:
Amount of water to be boiled off = Initial Volume - Final Volume
Amount of water to be boiled off = 6 liters - 3.6 liters
Amount of water to be boiled off = 2.4 liters
Therefore, you should boil off 2.4 liters of water from the initial 6 liters of brine in order to achieve a concentration of 200g/l.
To find out how many liters of water should be boiled off, we need to determine the initial mass of salt in the pot and the final mass of salt needed at a concentration of 200g/l.
First, let's calculate the initial mass of salt in the pot:
Initial mass of salt = concentration of brine * volume of brine
Given:
Concentration of brine = 120g/l
Volume of brine = 6 liters
Initial mass of salt = 120g/l * 6 liters = 720g
Next, let's calculate the final mass of salt required at a concentration of 200g/l:
Final mass of salt = concentration of brine * volume of brine
Given:
Concentration of brine = 200g/l
Final mass of salt = 200g/l * (6 liters - x)
We subtract x liters because we want to find the amount of water that needs to be boiled off, so the remaining volume of brine will be (6 liters - x).
Now, to maintain the same amount of salt, the initial and final masses of salt should be equal:
Initial mass of salt = Final mass of salt
720g = 200g/l * (6 liters - x)
Next, we can solve the equation for x:
720g = 200g/l * 6 liters - 200g/l * x
720g = 1200g - 200g/l * x
-480g = -200g/l * x
480g = 200g/l * x
Now, let's isolate x:
x = (480g / (200g/l)) * l
Cancel out the units:
x = (480g / 200) * l
x = 2.4 * l
Therefore, approximately 2.4 liters of water should be boiled off to achieve a concentration of 200g/l.