### Practice problems

**Though we’ve covered pharmaceutical calculation problems elsewhere, it’s vital that you practice each section to ensure you have an independent understanding of every problem type. **

The problem sheet below includes questions on unit conversions, mass-mole-molar mass relationships, dilutions and concentrations. If you’re unsure on any problem, take a few minutes to review the theorised examples we’ve covered on these topics.

You can find the answers to each problem at the bottom of this page. The mechanism of each answer has been omitted precisely because we want you to practice each problem rather than reading through and not critically thinking through each problem.

**Useful articles:**

**Numerical (metric) prefixes for units:**

**Other useful formulas:**

C_{1} = Concentration of the stock solution (more concentrated), V_{1} = Volume of the stock solution, C_{2} = Concentration of the working solution (more dilute), V_{2} = Volume of the working solution (final volume), DF = Dilution Factor.

### Questions:

**Q1. Perform the following conversions:**

a) 0.25 mL in µL

b) 324 mg in g

c) 0.45 mol/L in M

d) 195 J in kJ

e) -495 mV in V

f) 0.5 milliseconds in seconds

g) 40.46 g of RbCl in mol

h) 1250 ppm in ppb

i) 1.3 g/mL in kg/L

j) 4982 L.mol^{-1}.cm^{-1} in mL.mmol^{-1}.cm^{-1}

k) 7 °C in K

l) 8.5 atm in torr

m) 59.3 kGy in Gy

n) 625 µSv in Sv

o) 2.5 dm in cm

p) 10″ in cm

**Q2. Express the following in mol/L**

a) 0.35 M of aqueous NaOH

b) 1% w/v of L-(−)-Xylose (C_{5}H_{10}O_{5}) in 50 mL water.

c) 25 mM solution of aspirin

**Q3. You are provided with a stock solution of 0.05 M ATP.**

a) If you are required to perform a 1 in 25 dilution in a 50 mL volumetric flask, how much of the stock solution would you need?

b) What’s the concentration of the solution in Q3 a)?

**Q4. You are provided with a 50 ppm stock solution of Ca for GF-AA analysis.**

a) How much of the stock solution would you need to prepare a 25 ppb Ca solution in a 100 mL volumetric flask (in mL and µL)? What is the dilution factor?

b) How much of the stock solution would you need to prepare a 25 ppb Ca solution in a 250 mL volumetric flask (in mL and µL)? What is the dilution factor?

c) You were asked to perform a 20-fold dilution of the solution in Q4 b) in a 50 mL volumetric flask.

i. What is the dilution factor?

ii. How much of solution Q4 b) would you need to perform the dilution?

iii. What is the concentration, in ppb, of this new diluted solution?

iv. Express the concentration of the new diluted solution in ppm.

**Q5. You need to make up a 0.05 M stock solution of sodium carbonate (aqueous) in a 500 mL volumetric flask.**

a) Write the chemical formula of sodium carbonate.

b) Calculate the mass (g) of sodium carbonate required and name the required solvent.

c) Express 0.05 M in:

i. mol/L

ii. mol.L^{-1}

iii. g/L

iv. g/mL

v. mmol.L^{-1}

vi. mmol/mL

vii. mmol.mL^{-1}

viii. µM

ix. nM

d) Perform calculations to show how to prepare the following solutions serially starting from the stock solution of sodium carbonate if the required concentrations are: 0.001 M, 5.0×10^{-4} M, 1.0×10^{-4} M, 2.5×10^{-5} M. (Volume of the volumetric flasks = 50 mL)

e) Perform calculations to show how to do non-serial dilutions of the stock solution of sodium carbonate if the required concentrations are: 0.001 M, 5.0×10^{-4} M, 1.0×10^{-4} M, 2.5×10^{-5} M. (Volume of the volumetric flasks = 50 mL)

f) The 0.05 M stock solution of sodium carbonate was diluted to 0.0025 M in a 10 mL volumetric flask.

i. What is the dilution factor?

ii. How much of the stock solution is required to perform this dilution in:

i. mL

ii. L

iii. µL

g) A 1 in 40 dilution of 0.05 M stock solution was performed in a 20 mL volumetric flask.

i. What is the dilution factor?

ii. How much of the stock solution is required to perform this dilution?

iii. What is the concentration of this new diluted solution?

**Q6. You prepared a 0.001 M stock solution (150 mL) of ibuprofen (C _{13}H_{18}O_{2}). The solution was diluted to 5×10^{-5} M in a 50 mL volumetric flask.**

a) What is the dilution factor?

b) How much of the stock solution is required to perform this dilution in the 50 mL flask?

c) How many moles of ibuprofen is in the 150 mL 0.001 M stock solution?

d) How much ibuprofen (in g and in mg) was dissolved in the solvent in order to prepare 150 mL of the 0.001 M stock solution of ibuprofen?

**Q7. You are attempting to measure the T. pyriformis IGC50 of a new drug candidate as part of an ecotoxicity and environmental impact study. You are required to prepare solutions of the new drug candidate as part of the study.**

a) Show calculations for the preparation of a 100 mg/L stock solution of the test substance in a 250 mL volumetric flask.

b) 5 mL of the stock solution was diluted to 50 mL in a volumetric flask. What is the dilution factor?

c) If you are required to prepare a 1 in 5 dilution of the solution in Q7 b) in a 25 mL volumetric flask:

i. How much of the solution in Q7 b) do you need to perform this dilution?

ii. What is the concentration of this diluted solution in mg/L?

**Q8. Calculate the molar mass of the following drug molecules:**

a) Enasidenib (antineoplastic) C_{19}H_{17}F_{6}N_{7}O

b) Netarsudil (treatment of glaucoma) C_{28}H_{27}N_{3}O_{3}

c) Apalutamide (nonsteroidal antiandrogen) C_{21}H_{15}F_{4}N_{5}O_{2}S

d) Ozenoxacin (quinolone antibiotic)

e) Letermovir (treatment of cytomegalovirus (CMV) infections)

### Answers:

**Q1. Perform the following unit conversions:**

a) 250 µL

b) 0.324 g

c) 0.45 M

d) 0.195 kJ

e) -0.495 V

f) 0.0005 seconds

g) 0.335 mol

h) 1250000 ppb

i) 1.3 kg/L

j) 4982 mL.mmol^{-1}.cm^{-1}

k) 280.15 K

l) 6460 torr

m) 59300 Gy

n) 0.000625 Sv

o) 25 cm

p) 25.4 cm

**Q2. **

a) 0.35 mol/L

b) 0.0333 mol/L

c) 0.025 mol/L

**Q3. **

a) 2 mL

b) 0.002 M

**Q4.** 50 ppm = 50000 ppb

a) 0.05 mL, 50 µL, DF = 2000

b) 0.125 mL, 125 µL, DF = 2000

c)

i. DF = 20

ii. 2.5 mL

iii. 1.25 ppb

iv. 0.00125 ppm

**Q5.** 0.05 M

a) Na_{2}CO_{3}.

b) 2.6497 g, water.

c)

i. 0.05 mol/L

ii. 0.05 mol.L^{-1}

iii. 5.299 g/L

iv. 0.005299 g/mL

v. 50 mmol.L^{-1}

vi. 0.05 mmol/mL

vii. 0.05 mmol.mL^{-1}

viii. 50000 µM

ix. 50000000 nM

d) 1 mL, 25 mL, 10 mL, 12.5 mL.

e) 1 mL, 0.5 mL, 0.1 mL, 0.025 mL.

f)

i. DF = 20

ii.

i. 0.5 mL

ii. 0.0005 L

iii. 500 µL

g)

i. DF = 40

ii. 0.5 mL

iii. 0.00125 M

**Q6. **

a) DF = 20

b) 2.5 mL

c) 0.0001498 mol

d) 0.0309 g

**Q7. **

a) 0.025 g (25 mg)

b) DF = 10

c)

a. 5 mL

b. 2 mg/L

**Q8. **

a) Enasidenib: 473.38 g.mol^{-1}

b) Netarsudil: 453.54 g.mol^{-1}

c) Apalutamide: 477.435 g.mol^{-1}

d) Ozenoxacin: 363.42 g.mol^{-1}

e) Letermovir: 572.56 g.mol^{-1}