A certain brine has 3.96% NaCl by mass. A 75.0−mL sample weighs 76.7g How many liters of this solution should be evaporated to dryness to obtain 730kg NaCl?

The old molarity formula.

density x mL x %/100 = grams.
The density of the solution is d = mass/volume = 76.7/75.0 = whatever, then
(76.7/75.0) x ? mL x 0.0396 = 730,000
Solve for ?mL and convert to L.

18037.5L

1.83 x 10^4 L

Well, I certainly wouldn't recommend drinking that solution. It sounds a bit salty to me! But let's get to work on the calculations.

First, let's find the mass of NaCl in the 75.0 mL sample. Since the sample has a mass of 76.7 g and is 3.96% NaCl, we can multiply the mass by the percentage to find the mass of NaCl:

76.7 g × 0.0396 (3.96% as a decimal) = 3.03672 g NaCl

Next, we need to determine the concentration of NaCl in the solution. Since the sample is 75.0 mL and contains 3.03672 g of NaCl:

3.03672 g NaCl / 75.0 mL = 0.0404909333 g/mL

Now we can use this concentration to find the volume of the solution needed to obtain 730 kg of NaCl. But first, we need to convert 730 kg to grams:

730 kg × 1000 g/kg = 730,000 g

Since the concentration is given in g/mL, we can rearrange the equation to solve for volume:

0.0404909333 g/mL = 730,000 g / V (V represents volume)

Now, let's solve for V:

V = 730,000 g / 0.0404909333 g/mL = 18,011,688.9 mL

Converting this to liters, we divide by 1000:

18,011,688.9 mL / 1000 = 18,011.6889 L

So, you would need to evaporate approximately 18,011.7 liters of the solution to obtain 730 kg of NaCl. That's quite a lot! Better grab a really big evaporation dish.

To solve this problem, we need to determine the amount of NaCl in the brine solution and then calculate the volume of solution that needs to be evaporated to obtain the desired amount of NaCl.

Step 1: Calculate the mass of NaCl in the 75.0 mL sample.
Given that the brine has 3.96% NaCl by mass and the sample weighs 76.7 g, we can calculate the mass of NaCl in the sample as follows:
Mass of NaCl = (3.96/100) * 76.7 g
Mass of NaCl = 3.03752 g

Step 2: Calculate the amount of NaCl in the entire solution.
To determine the amount of NaCl in the entire solution, we need to set up a proportion using the mass of NaCl in the sample and the total volume of the solution. The proportion is as follows:
(3.03752 g)/(75.0 mL) = (x g)/(volume of solution)
From the given information, we know that the desired amount of NaCl is 730 kg. So, we need to convert it to grams:
Desired amount of NaCl = 730 kg * 1000 g/kg = 730,000 g

Solving the proportion, we get:
x = (3.03752 g * (volume of solution))/(75.0 mL)
Simplifying, we have:
x = (3.03752 g * volume of solution)/0.0750 L
Since the units of volume on the right side are in liters, we need to convert the given sample volume to liters too:
75.0 mL = 75.0 mL * (1 L/1000 mL) = 0.0750 L

Now, we can substitute the values in the equation:
730,000 g = (3.03752 g * volume of solution)/0.0750 L

Step 3: Solve for the volume of solution.
To isolate the variable "volume of solution," we can cross multiply and then divide both sides of the equation by 3.03752:
volume of solution = (730,000 g * 0.0750 L) / 3.03752 g

Calculating the expression on the right side, we get:
volume of solution = 18,150 L

Therefore, approximately 18,150 liters of the solution should be evaporated to dryness in order to obtain 730 kg of NaCl.