(NaCl) solutions used in intravenous injections have a concentration of 0.90% NaCl (mass/volume).
4.5grams of NaCl are needed to prepare 500.0 mL of this solution
How much water must evaporate from this solution to give a solution that is 9.0% NaCl (mass/volume)?
a mL of water is a gram
4.5 / x = .09
x = 50 grams water remains
so 450 grams evaporated
To solve this problem, we will use the concept of mass percent and the relationship between mass and volume.
Step 1: Calculate the initial mass of the solution
Given that the concentration of NaCl in the initial solution is 0.90%, we can find the initial mass of NaCl using the formula:
Mass = Concentration * Volume
Mass = 0.90% * 500.0 mL = 0.009 * 500.0 g = 4.5 g
So, the initial mass of the NaCl in the solution is 4.5 grams.
Step 2: Calculate the initial mass of water in the solution
To find the initial mass of water in the solution, subtract the mass of NaCl from the total mass of the solution.
Total mass of the solution = Mass of NaCl + Mass of water
Mass of water = Total mass of the solution - Mass of NaCl
Mass of water = 500.0 g - 4.5 g = 495.5 g
So, the initial mass of water in the solution is 495.5 grams.
Step 3: Calculate the final mass of NaCl in the solution
Given that we want to have a final concentration of 9.0%, we can calculate the final mass of NaCl using the same formula as in Step 1.
Mass of NaCl = Concentration * Volume
Mass of NaCl = 9.0% * 500.0 mL = 0.09 * 500.0 g = 45 g
Step 4: Calculate the final mass of water in the solution
To calculate the final mass of water in the solution, subtract the mass of NaCl from the total mass of the solution.
Total mass of the solution = Mass of NaCl + Mass of water
Mass of water = Total mass of the solution - Mass of NaCl
Mass of water = 500.0 g - 45 g = 455 g
Step 5: Calculate the amount of water that must evaporate
The amount of water that must evaporate is the initial mass of water minus the final mass of water.
Amount of water evaporated = Initial mass of water - Final mass of water
Amount of water evaporated = 495.5 g - 455 g = 40.5 g
Therefore, 40.5 grams of water must evaporate from the solution to obtain a solution that is 9.0% NaCl (mass/volume).