An ice-bath made with sodium chloride will be 9 ± 1 oC when the solution is about 23% sodium chloride by mass. The density of solid sodium chloride is about 2 g/cm3. What volume of solid NaCl would you add to 200 g water to make a 23% NaCl solution?
ANY HELP WOULD BE AWESOME!THANK YOU!! :)
23% NaCl is 23 g NaCl/100 g solution.
so 200 g soln is 46g NaCl.
mass = volume x density so
volume = mass/density = 46/2 = ? cc.
I got 23...but the answers available are a. 10 mL
b. 30 mL
c. 50 mL
d. 100 mL ... is there something that I am doing incorrectly?
my error. I read that as 200 g SOLUTION but it is 200 g H2O
23% NaCl is 23 g/100 g solution which is 23 g NaCl in 77 g H2O. grams NaCl in 200 g H2O is 23 x 200/77 = ?
and ?/2 = ?cc.
I got 30 this time! Yay! Thank you so much DrBob222! I really appreciate it!
To find the volume of solid NaCl needed to make a 23% NaCl solution, we need to consider the density of solid sodium chloride and the mass of water.
Let's break down the problem step by step:
1. Find the mass of sodium chloride required:
Mass of NaCl = Mass of solution × Percentage of NaCl / 100
In this case, the mass of the solution is the sum of the mass of water and the mass of sodium chloride:
Mass of solution = Mass of water + Mass of NaCl
2. Calculate the mass of water:
Given: Mass of water = 200 g
3. Calculate the mass of sodium chloride:
Mass of NaCl = Mass of solution × Percentage of NaCl / 100
Mass of NaCl = (Mass of water + Mass of NaCl) × Percentage of NaCl / 100
4. Rearrange the equation to solve for the mass of NaCl:
Mass of NaCl - (Percentage of NaCl / 100) × Mass of NaCl = Mass of water × (Percentage of NaCl / 100)
Mass of NaCl × (1 - Percentage of NaCl / 100) = Mass of water × (Percentage of NaCl / 100)
Mass of NaCl = (Mass of water × (Percentage of NaCl / 100)) / (1 - Percentage of NaCl / 100)
5. Substitute the given values:
Mass of NaCl = (200 g × (23 / 100)) / (1 - (23 / 100))
6. Calculate the mass of NaCl:
Mass of NaCl = (46 g) / (0.77)
Mass of NaCl ≈ 59.74 g
7. Calculate the volume of solid NaCl using its density:
Density = Mass / Volume
Volume = Mass / Density
Given: Density of solid NaCl = 2 g/cm^3
Volume of solid NaCl = Mass of NaCl / Density
Volume of solid NaCl = 59.74 g / 2 g/cm^3
Volume of solid NaCl ≈ 29.87 cm^3
Therefore, you would need approximately 29.87 cm^3 (cubic centimeters) of solid NaCl to add to 200 g of water to make a 23% NaCl solution.