In each of the following, determine how much solute (in g or mL) must be added to the correct quantity of water to make the given amount of solution at the correct concentration.
a)KI to make 50.0mL of a 0.50 M solutioon
b)12.0 M HCL to make 500 mL of a 1.0 M HCl
c)Sucrose (C12 H22 O11) to make 1.0 kg of a 5% sucrose (by mass) solution
d)1.0M NaCl to make 100.0 mL of 0.10 M NaCl
All of these are done strictly by definition. If you know the definition you should be able to do the problem.
Here is the first one. Try the others on your own.
a)
M = moles/L.
Therefore, moles = M x L
We want 0.50M x 0.050 L = 0.025 moles.
moles = grams/molar mass and we rearrange to grams = moles x molar mass.
0.025 moles x molar mass KI = grams KI.
The others all follows this type solution (no pun intended) although they will vary somewhat depending upon the definition of the solution.
To determine the amount of solute needed to make a specific solution with a given concentration, we can use the formula:
mass of solute = concentration x volume of solution
or
V1C1 = V2C2
where:
V1 = volume of solution 1 (given)
C1 = concentration of solution 1 (given)
V2 = volume of solution 2 (desired)
C2 = concentration of solution 2 (desired)
Let's solve each part of the question step by step:
a) KI to make 50.0 mL of a 0.50 M solution:
Given:
V1 = unknown (to be calculated)
C1 = 0.50 M
V2 = 50.0 mL
C2 = unknown
Using the formula V1C1 = V2C2, we can rearrange it to solve for V1 (unknown):
V1 = (V2C2) / C1
V1 = (50.0 mL x 0.50 M) / 0.50 M
V1 = 25.0 mL
Therefore, 25.0 mL of KI should be added to 50.0 mL of water to make a 0.50 M solution.
b) 12.0 M HCl to make 500 mL of a 1.0 M HCl:
Given:
V1 = unknown (to be calculated)
C1 = 12.0 M
V2 = 500 mL
C2 = 1.0 M
Using V1C1 = V2C2, solve for V1:
V1 = (V2C2) / C1
V1 = (500 mL x 1.0 M) / 12.0 M
V1 = 41.7 mL
So, 41.7 mL of 12.0 M HCl should be added to 500 mL of water to make a 1.0 M HCl solution.
c) Sucrose (C12 H22 O11) to make 1.0 kg of a 5% sucrose solution (by mass):
Given:
V1 = unknown (to be calculated)
C1 = unknown
V2 = 1.0 kg
C2 = 5% (by mass)
To solve this, we need to calculate the mass of sucrose needed:
mass of solute = mass of solution x % concentration (by mass)
mass of solute = (V2 x C2) / 100
mass of solute = (1.0 kg x 5%) / 100
mass of solute = 0.05 kg
Now, we need to convert the mass of sucrose to volume using its density. Let's assume the density of sucrose is 1.59 g/mL:
volume of solute = mass of solute / density
volume of solute = 0.05 kg / 1.59 g/mL
volume of solute ≈ 31.5 mL
So, approximately 31.5 mL of sucrose should be added to 1.0 kg of water to make a 5% sucrose solution.
d) 1.0 M NaCl to make 100.0 mL of 0.10 M NaCl:
Given:
V1 = unknown (to be calculated)
C1 = 1.0 M
V2 = 100.0 mL
C2 = 0.10 M
Using V1C1 = V2C2, solve for V1:
V1 = (V2C2) / C1
V1 = (100.0 mL x 0.10 M) / 1.0 M
V1 = 10.0 mL
Therefore, 10.0 mL of 1.0 M NaCl should be added to 100.0 mL of water to make a 0.10 M NaCl solution.