1. Maths and Chemistry for Biologists

2. Chemistry Examples 1 This section of the course gives worked examples of the material covered in Chemistry 1 and Chemistry 2

3. Moles In all of the following use the approximate A r values H = 1; C = 12; N = 14; O = 16; Na = 23; P = 31; Cl = 35.5; K = 39 What is the relative molar mass (M r ) of CH 3 COOH? Simply add the A r values of the constituent atoms M r = (12 x 2) + (16 x 2) + (1 x 4) = 60

4. What mass of the substance NH 2 CH 2 COOH (glycine) is 0.1 mol? A mole of a compound has a mass equal to the M r of that compound. The M r of glycine is (12 x 2) + 14 + (16 x 2) + (5 x 1) = 75 Hence 1 mol is 75 g and 0.1 mol = 7.5 g

5. Carbon burns in oxygen to give carbon dioxide according to the equation C + O 2  CO 2 What weight of O 2 would react with 1 g of carbon? 1 mol (12 g) of carbon reacts with 1 mol (32 g) of oxygen molecules. Hence 1 g of carbon reacts with 32/12 = 2.67 g O 2 (Alternatively, 1 g of carbon is 1/12 = 0.083 mol. This reacts with 0.083 mol of O 2 which is 32 x 0.083 = 2.67 g)

6. Solutions What would be the molar concentration of a solution containing 10 g of KH 2 PO 4 in 500 ml? The basic definition is that a solution containing 1 mol of solute in 1 L of solution has a concentration of 1 M The solution here contains 10 g in 500 ml or 20 g/L. The M r of KH 2 PO 4 is 136. So 20 g is 20/136 = 0.147 mol and the concentration is 0.147 M

7. What weight of NaCl would there be in 1 ml of a 0.5 M solution? A 0.5 M solution contains 0.5 mol of solute per litre or 0.5 mmol/ml The M r of NaCl is 23 + 35.5 = 58.5 Hence 0.5 mmol is 58.5 x 0.5 x 10 -3 = 0.0293 g or 29.3 mg

8. What is the molarity of a 0.9% (w/v) solution of NaCl? A 0.9% (w/v) solution contains 0.9 g of solute/100 ml of solution or 9 g/L The M r of NaCl is 58.5 Hence the concentration is 9/58.5 = 0.154 M or 154 mM

9. A solution has a concentration of 0.15 mM. Express this concentration in terms of a) M and b)  M a)0.15 x 10 -3 M or 1.5 x 10 -4 M (the unit M is 10 3 times bigger than the unit mM so we have a number of them that is 10 3 times smaller. Think of it in familiar terms: if your finger is 50 mm long, is it 50 x 10 3 m long or 50 x 10 -3 m long?) b)0.15 x 10 3  M or 150  M (in this case the unit  M is 10 3 times smaller than the unit mM so the number is 10 3 times bigger)

10. What would be the concentration if 10 ml of a 0.25 M solution were diluted to a final volume of 500 ml? The dilution is 50-fold so the concentration goes down by a factor of 50. Hence concentration is 0.25/50 = 0.005 M or 5 mM

11. How many  mol of NaCl would there be in 100  l of a 2.5 M solution? A 2.5 M solution contains 2.5 mol/l or 2.5  mol/  l. Hence 100  l of the solution contains 250  mol

12. A protein solution has a concentration of 1 mg/ml and the M r of the protein is 50,000. a) what is the concentration in units of  M b) how many molecules of protein would there be in 1  l of solution? a) The concentration is 1 mg/ml or 1 g/l. 1 g of the protein is 1/50,000 of a mol or 20 x 10 -6 mol or 20  mol. Hence the concentration is 20  M. b) The solution contains 20  mol of protein/L or 20 x 10 -6 mol/l. Hence in 1  l there will be 20 x 10 -12 mol. 1 mol of substance contains 6.02 x 10 23 molecules (the Avogadro number) therefore 20 x 10 -12 mol will contain 6.02 x 10 23 x 20 x 10 -12 = 1.204 x 10 13 molecules

13. What weight (in  g) of protein would there be in 10  l of a solution of concentration 10 mg/ml? Concentration is 10 mg/ml or 10  g/  l. Hence there will be 100  g in 10  l

14. A drug sample for bioassay is prepared at a concentration of 1 mM (sample A). Sample B is prepared by taking 100  l of sample A and adding it to 900  l of buffer. Sample C is prepared by taking 100  l of sample B and adding it to 900  l of buffer. Sample D is prepared by taking 100  l of sample C and adding it to 900  l of buffer. What are the concentrations of samples B, C and D? At each step there is a dilution by a factor of 10 (100  l in a total of 1000  l) and the concentrations will be B: 0.1 mM or 100  M C: 0.01 mM or 10  M D: 0.001 mM or 1  M