Molar Concentrations
How much arginine do you need to make a 0.01M solution of arg?
MW of Arg: 174.20 g/mol
You weight 1.742 g of arg and add diluent up to the 1 L mark.
Solution:
174.20 g/mol x 0.01 mol/L = 1.742 g
How much NaCl would you need to weigh out to create 1L of 0.9% NaCl solution?
Assuming density is 1 g/ml
What is 9g of NaCl.
Mass of NaCl=(Percentage concentration/100) ×Volume of solution×Density of solution
mass = 0.009 x 1000 x 1
mass = 9
Prepare 50 mL of a 3% solution from a 4% solution in one step. 🧍
50/4 = 12.5 mL x 3 = 37.5 mL
What is taking 37.5 mL of the 4% solution and add diluent up to the 50 mL mark ⛹️
How would you prepare 1 ml of a 1:5 dilution of sera?
A 1:5 dilution means 1 part serum + 4 parts diluent.
Serum volume:
(1/5) x 1 mL = 0.2 mL
Diluent volume:
1 - 0.2 = 0.8 mL
Mix:
0.2 mL serum + 0.8 mL diluent → 1 mL of 1:5
If 0.1 mL of a urine culture from a 10-6 dilution yielded 38 colonies, how many bacteria were there in the original sample?
Answer should be in CFU/mL.
[A CFU (colony-forming unit) represents one viable bacterium capable of growing into a visible colony.]
CFU/mL = (number of colonies/volume plated in mL) x dilution factor
CFU/mL = 38/0.1 x 10^6
= 3.8 x 10^8 CFU/mL
How would you make 500 mL of a 0.05 M NaCl solution?
MW of NaCl: 58.44 g/mol
Answer in this format:
You weigh _____ g of NaCl and add diluent up to the ____ mL mark.
You weigh 1.461 g of NaCl and add diluent up to the 500 mL mark.
Solution:
1M NaCl = 1 mol/L = 58.44 g/L
58.44 g/L x 0.5 L = 29.22 g
29.22 g x 0.05 = 1.461 g
If a 500ml solution was reported to have a 15% concentration of X substance, how much X in g is in the solution?
Assume density is 1g/ml
What is 75g.
Mass of X=(Percentage concentration/100) ×Volume of solution×Density of solution
mass= 0.15 x 500 x 1
mass = 75
Prepare 100 mL of 10% alcohol from 95% alcohol in one step. 🙀
(100 mL) (10%) = (x mL) (95%)
x = 10.5 mL
What is taking 10.5 mL of the 95% alcohol solution and adding diluent up to the 100 mL mark 😾
How would you prepare 8 mL of a 1:20 dilution of sera?
A 1:20 dilution means 1 part serum + 19 parts diluent.
Serum volume:
(1/20) × 8 mL = 0.4 mL
Diluent volume:
8 − 0.4 = 7.6 mL
Mix:
0.4 mL serum + 7.6 mL diluent → 8 mL of 1:20
Quick lesson!
What is a CFU?
A CFU (colony-forming unit) represents one viable bacterium capable of growing into a visible colony. Plates with 30-300 colonies are considered countable. <30 have high statistical error, >300 suffer from colony overlap.
So...
How many bacteria were present in the original sample?
Dilution Volume Plated # of Colonies
10-2 0.1 mL 241
10-3 0.1 mL 35
10-4 0.1 mL 7
10-5 0.1 mL 0
CFU/mL = (number of colonies/volume plated in mL) x dilution factor
Step 1: Calculate CFU/mL from each countable plate
241/0.1 x 102 = 2.41 x 105 CFU/mL
35/0.1 x 103 = 3.5 x 105 CFU/mL
Step 2: Average the two values
(2.41 x 105 + 3.5 x 105)/2
= 2.95 x 105 CFU/mL
A cell culture protocol requires DMEM supplemented with 25 mM glucose. If you are preparing 1.0 L of media and the molar mass of glucose (C₆H₁₂O₆) is 180 g/mol, how many grams of glucose must be added to achieve the required concentration?
You must add 4.5 grams of glucose to 1.0 L of DMEM to achieve a 25 mM glucose concentration.
Solution:
1. 25 mM=0.025 M
2. moles=M×V=0.025 mol/L×1.0 L=0.025 mol
3. grams=0.025 mol×180 g/mol=4.5 g
If a solution was created using 50g of substance X and filling the remaining 750 ml beaker with DI water, what is the concentration of substance X in this solution?
assume density 1g/ml
What is approximately 6.67?
Concentration = (mass of X/ Total volume) x 100
concentration = (50/750) x 100
concentration = 6.67
Volume of a 0.02% solution that can be prepared from 25 mL of a 0.1% solution 🤫
(25 mL) (0.1%) = (x mL) ( 0.02%)
x = 125 mL
What is 125 mL 🐐
You have a stock solution of protein containing 10 g/ml. You want a solution with a final concentration of 2 mg/ml. How would you perform this dilution in just three steps?
First convert units:
10 g/mL = 10,000 mg/mL
Overall dilution factor:
10,000 ÷ 2 = 1:5,000
One possible three-step dilution:
1:100 → 1:10 → 1:5
Step 1 (1:100):
0.01 ml stock + 0.99 mL diluent → 100 mg/mL
Step 2 (1:10):
0.1 mL of Step 1 + 0.90 mL diluent → 10 mg/mL
Step 3 (1:5):
0.2 mL of Step 2 + 0.8 mL diluent → 2 mg/mL (final)
Image Based Question 1
Step 1: Calculate total dilution
10 x 10 x 10 x 10 = 10-4 dilution
This is because-
1/1+9 = 1/10
Step 2: Apply formula
CFU/mL = (number of colonies/volume plated in mL) x dilution factor
201/1 x 104 =
2.01 x 106 CFU/mL
What is the molarity of a solution that was prepared by dissolving 14.2 g of NaNO3 in enough water to make 350 mL of solution?
MW of NaNO3: 85 g/mol
0.477 M
Solution:
14.2 g x 1 mol/85 g x 1/0.35L = 0.477 M
If a 1000ml solution was created using 50g of substance X, 70g of substance Y, and filled the remainder of the beaker with DI water, what are the concentrations of the two substances in the solution?
assuming density 1g/ml
What is 5% of X and 7% of Y.
Concentration of X: Concentration of X (%)=(50g/1000 ml)×100
Simplify the calculation: Concentration of X (%)=5%
Concentration of Y: Concentration of Y (%)=(70g/1000 ml)×100
Simplify the calculation: Concentration of Y (%)=7%
Percent concentration of alcohol prepared when 10 mL of 95% alcohol are diluted with H2O to make a final volume of 38 mL 🦧
(10 mL) (95%) = (38 mL)(x%)
x = 25%
What is 25% concentration of alcohol 🦍
You have a stock solution of 10 mg/ml of vitamins. You want a solution with a final concentration of of 0.5 ug/ml. How would you perform this dilution in just three steps?
Convert units:
10 mg/mL = 10,000 µg/mL
Overall dilution factor:
10,000 ÷ 0.5 = 1:20,000
One possible three-step dilution:
1:100 → 1:100 → 1:2
Step 1 (1:100):
10 µL stock + 990 µL diluent → 100 µg/mL
Step 2 (1:100):
10 µL of Step 1 + 990 µL diluent → 1 µg/mL
Step 3 (1:2):
500 µL of Step 2 + 500 µL diluent → 0.5 µg/mL (final)
Image Based Question 5
Each transfer is a 1:100 dilution. So, 100 x 100 x 100 = 10-6 dilution
CFU/mL = (number of colonies/volume plated in mL) x dilution factor
CFU/mL = 46/0.1 x 106 =
4.6 x 108 CFU/mL
0.172 M
Solution:
1. Calculate molarity of stock solution (0.69M)
2. Figure out how many mol of Na₂CO₃ are in the 100mL solution (0.069 mol)
3. Calculate final molarity of solution (0.172M)
Someone with short-term memory loss created a solution using 18g of substance X and forgot how much DI water they put in but remembered that the concentration of X was 20%. What was the total volume of the initial solution?
Assume density is 1g/ml
What is 90ml
concentration = (mass of x/total volume) x density
20% = (18/total volume) x 1
0.2 = 18/total
total = 90
Percentage of dextrose that is prepared when 3 mL of a 10% dextrose solution are mixed with 12 mL of broth 😟
(3 mL) (10%) = (3 + 10 mL) (x%)
x = 2%
What is 2% dextrose solution 😍
You want 4 mL of a 1:128 dilution of serum. How would you perform this dilution in two steps?
Break the dilution into steps:
1:8 × 1:16 = 1:128
Step 1 (1:8):
0.5 mL serum + 3.5 mL diluent → 4 mL of 1:8
Step 2 (1:16):
0.25 mL of 1:8 + 3.75 mL diluent → 4 mL of 1:128
Image Based Question 6
Step 1: Calculate total dilution
10 x 10 x 10 x 100 x 10 x 10 = 10-7 dilution
This is because-
1/1+9 = 1/10
0.5/0.5+4.5 = 1/10
3/27+3 = 1/10
1/1+99 = 1/100
1/9+1 = 1/10
2/18+2 = 1/10
10 x 10 x 10 x 100 x 10 x 10 = 10-7 dilution
Step 2: Apply formula
CFU/mL = (number of colonies/volume plated in mL) x dilution factor
84/0.01 x 107 =
8.4 x 1010 CFU/mL