W3 Pharmaceutical calculations Flashcards
inc lecture and workshop notes
- od
- tds, tid
once daily
three times a day
bd, bds, bid
qds, qid
twice a day
four times a day
ii qds prn mdu
two tablets, four times a day, when required, as directed
i, ii and iii
Examples?
1,2,3 tablet (s) Eye drops, inhalations etc
om, mane, am
on, nocte, pm
In the morning
At night
Prn,sos
When required/if necessary
Mdu, ud
As directed/use as directed
qld
qod, alt
Mitt. Mitte, send
Once daily
On alternate days
Total quantity
qh, q1h
q2h
q4h or qqh
q12h
stat.
Hourly
Every two hours
Every four hours
Every twelve hours
Immediately
1 kilogram in grams?
1000 grams (g)
1 gram in milligrams?
1000 milligrams (mg)
1mg in mcg?
1000 micrograms (mcg)
1mcg in nanograms?
1000 (ng)
Which are bigger?
Nanograms
milligrams
micrograms
Milligrams > Micrograms > Nanograms
10- 3 > 10-6 > 10-9
1 litre in millilitres
1mL in microlitres?
microlitres is NOT mL (millilitres)
1L= 1000 millilitres
1mL=1000 microlitres
What are solid dosage forms measured in?
grams, milligrams,micrograms
What are non-solid dosage forms measured in?
milligrams/mL
e.g. 100mg/5ml or 10mg/ml
Non solid dosage forms:
What do (% w/v) (% v/v) (%w/w) mean??
- weight in volume (% w/v): % = g per 100ml [e.g. 2% = 2g per 100ml]
- volume in volume (% v/v): % = ml per 100ml [e.g. 2% = 2ml per 100ml]
- weight in weight (% w/w): %= g per 100g
Non solid dosage forms:
What do (% w/v) (% v/v) (%w/w) mean??
- weight in volume (% w/v): % = g per 100ml [e.g. 2% = 2g per 100ml]
- volume in volume (% v/v): % = ml per 100ml [e.g. 2% = 2ml per 100ml]
- weight in weight (% w/w): % = g per 100g [e.g. 2% = 2g per 100g]
Ratios:
What is; 1:1000 and 1:10,000
1:1000= 1g in 1000ml
1:10,000= 1g in 10,000ml
What is the definition of dose?
The amount of medicine taken by/administered to a patient in order to achieve a therapeutic outcome.
1)A patient is prescribed amoxicillin capsules 250mg 1 tds x 7 days.
a. How many capsules should we dispense?
b. How many grams of amoxicillin do they take if they complete the course?
The same patient needs amoxicillin suspension 250mg/5ml instead of capsules.
a. How many millilitres of suspension would we dispense to cover the full course?
b. What strength (%w/v) is this suspension?
a: 21 capsules
b: 21x250= 5,250mg= 5.25g
a. 5ml x 3 x 7 =105mL
b. 250mg/5mL
100/5= 20
250x20= 5,000
5000mg/100mL
so, 5g/100mL so 5% w/v
Doses based on renal function:
When does a dose need to be decreased?
What can renal function be expressed as? (2)
When there is a reduction in kidney function
eGFR- estimated Glomerular Filtration Rate
Creatinine clearance
Creatinine clearance; things to remember (3):
Creatinine clearance (ml/min) = (140-age) x weight x constant/ serum creatinine
Do brackets first
Constant is different for males and females:
1.23 for male and 1.04 for female (micro mol/l)
Age in years, weight in kg,
Mrs Mitra is a 67 year old patient who weighs 70kg. Her recent bloods show a serum creatinine of 90 micromol/L
constant=
Work out her creatinine clearance: (use GpHC approved calculator)
Creatinine clearance (ml/min) = (140-age) x weight x constant/ serum creatinine
59.05
“Parts” in formulae and dilutions:
(for info)
- Industrial methylated spirit (IMS), BP
- spirit (L) 95 parts
- wood naphtha (L) 5 parts
For IMS above, the formula adds up to 100 parts.
To make 200L of IMS, you would use
* 95L x 2 = 190L of spirit
* 5L x 2 = 10L of wood naphtha
Differentiate between “parts” and “to
parts”
Example 1
* calamine powder 1 part
* aqueous cream to 10 parts
Example 2
* calamine powder 1 part
* aqueous cream 10 parts
Example 1: Equivalent to:
1g
9g
Total: 10g and (1g/10g) x 100% = 10% w/w
Example 2:
Equivalent to:
1g
10g
Total: 11g and (1g/11g) x 100% = 9.09% w/w
A prescription calls for 10ml qds x 7 days. How many millilitres do you supply?
=280 ml
10x4x7
A patient takes digoxin tablets 250 micrograms od. How many milligrams of digoxin do they take in a month (28 days)?
= 7 milligrams
250 x 28= 7000mcg / 1000= 7mg
A patient uses chloramphenicol eye drops 1% (w/v), 1 drop q2h (during waking hours – for this example 16 hours per day) for two days and 1 drop qds for the next three days. Each drop is 0.05ml.
i) How many millilitres has the patient used?
ii) How many milligrams has the patient used?
i) (9x2) +(4x3)= 30 eye drops x0.05ml
= 1.5ml
ii) 1.5ml
1% w/v= 1g in 100ml
1.5/100= 0.015g so 15 milligrams
8 can be used instead of 9
How many grams of active ingredient are contained in 1L of a 5% w/v solution?
=50g
- 5%w/v = 5g/100mL
- (1000mL/100mL) x 5g = 50g
What strength, expressed as w/v, is paracetamol suspension 120mg/5ml?
= 2.4% w/v
- w/v means g/100mL
- (100mL/5mL) x 120mg = 2400mg = 2.4g
- If there are 2.4g in 100mL, strength is 2.4%w/v
How many grams of amoxicillin would a patient take in total if they were prescribed:
Amoxicillin Capsules 500mg tds x 5 days?
=7.5g
- 500mg tds means 500mg three times a day = 1500mg daily
- Given for 5 days = 7500mg = 7.5g
What volume of adrenaline 1 in 1000 would need to be administered to provide a 300mcg dose?
=0.3ml
- 1 in 1000 means 1g in 1000ml
- 1g in 1000ml = 1000mg in 1000ml = 1mg/ml = 1000mcg/ml
- Want 300mcg, so (300mcg/1000mcg) x 1ml = 0.3ml
How much of each ingredient is required to make 250ml of Chalk Mixture, Paediatric BP?
* chalk 20g
* tragacanth powder 2g
* cinnamon water, conc 4ml
* syrup 100ml
* chloroform water, double strength 500ml
* water to 1000ml
Need 250ml/1000ml = 0.25 times (a quarter) of each ingredient.
- chalk 50g
- tragacanth powder 0.5g or 500mg
- cinnamon water, conc 1ml
- syrup 25ml
- chloroform water, double strength 125ml
- water to 250ml
When may we need to change to strength of a medicine?
Reasons for decreasing and increasing?
Decrease – e.g. for administration to a child or an older patient or for preparation of a medicine to give to a patient from a stock solution. This is done by dilution.
Increase – e.g. to make a product that is stronger than the one we have available. This is done by admixing (the action of adding one ingredient to something else)
When we dilute:
the amount of active ingredient inc/dec ..?
the concentration inc/dec ..?
Stays the same
Decreases
We have a 20% w/v of stock solution and want to make 200ml of a 5% w/v solution.
-How much stock solution and how much diluent do we need?
2 methods to work out; C1V1=C2V2 or First principles
Stock- 20% w/v = 20g in 100ml
Product- 5% w/v= 5g in 100ml (200ml)
10g active ingredient in 200ml x2
so 50ml of stock (half) is needed for 10g and 150ml diluent to make 200ml
You have a 25% stock solution and need to make 1L of a 1% preparation. How much stock solution and how much diluent do you need?
40ml stock and 960ml of diluent
Using the equation C1V1 = C2V2
25% x V1 = 1% x 1000ml So, V1 = (1%/25%) x 1000ml =40ml
You need to make 50ml of a 7.5% w/v solution. You have a 12% w/v solution in stock. How much stock and how much diluent do you need?
31.25ml stock and 18.75ml of diluent
Using the equation C1V1 = C2V2
12% x V1 = 7.5% x 50ml
So, V1 = (7.5%/12%) x 50ml = 31.25ml
18.75 diluent
You need to make a 150ml of a 1.25mg/5ml solution. You have a 1.5% w/v solution in stock. How much stock and how much diluent do you need?
2.5ml stock, 147.5ml diluent
1.25mg/5ml = 25mg/100ml = 0.025g/100ml = 0.025% w/v Then, V1 = (0.025%/1.5%) x 150ml = 2.5ml
You have a 10ml of a 4% solution. How many 1ml ampoules of a 1 in 1000 solution could you make?
1 in 1000 = 1g in 1000ml = 0.1g/100ml = 0.1% w/v
4% x 10ml = 0.1% x V2
So, V2 = (4%/0.1%) x 10ml = 400ml
400 x 1ml ampoules
If we can make 400ml of 1 in 1000 solution, we can fill 400 x 1ml amps
Multiple/Serial Dilutions:
What weight of active ingredient is required to produce 1000ml of a solution such that, when 2.5ml is diluted to 50ml with water, it gives a 0.25% w/v solution?
= 50g
Stock Solution Product
5% w/v 0.25% w/v = 0.25g per 100ml
= 5g per 100ml
20x dilution
- 0.25% = 0.25g/100ml, so final product 50ml contains 0.125g (as it did
2.5ml before dilution) - So: if there is 0.125g in 2.5ml of original solution, we need:
(1000ml/2.5ml) x 0.125g = 50g to make 1000ml of stock
method 2:
* Diluted 50ml/2.5ml = 20 times
* Original solution must therefore be 20 x 0.25% w/v = 5% w/v
* 5% w/v = 5g/100ml
* So, need: (1000ml/100ml) x 5g = 50g active ingredient to make 1000ml
What weight of active ingredient is required to produce 250ml of a solution such that, when 10ml is diluted to 200ml, we have a 1% w/v solution?
Solution is diluted 200ml/10ml = 20 times
* So, original solution is 20 x 1% w/v = 20% w/v
* 20% w/v = 20g in 100ml
* To make 250ml, need (250ml/100ml) x 20g = 50g
or 20g x 2.5=50g
What are the different types of dose?
Single dose, Daily dose, Daily divided dose, Weekly dose
Examples of doses based on weight: (for info)
- Can often be for children, but also for specific medicines in adults.
- Expressed as mg/kg or mcg/kg for weight
e.g. Paracetamol - Expressed as mg/m2 or mcg/m2 for BSA
- Often there is an accompanying maximum dose that should not be exceeded.
For infusions: the dose if often expressed as:
mg/kg/min or mcg/kg/min
A patient, weight 68kg, has been diagnosed with viral encephalitis and requires aciclovir at a dose of 10mg/kg every 8 hours. What total dose is required?
68kg x 10mg/kg = 680mg every 8 hours
A child aged 2, weight 12kg, has asthma and requires a 3 day course of steroids. The dose of prednisolone would be 1-2mg/kg od. What dose range could be administered?
12-24 mg od x 3 days
The maintenance dose of sodium valproate for epilepsy in children is 30mg/kg daily in two divided doses.
i) What is the dose in mg for a 12kg child?
ii) Sodium valproate is available as a 200mg/5ml oral solution. What is the dose in ml?
- 12kg x 30mg/kg = 360mg per day
In two divided doses, this is 180mg bd - (180mg/200mg) x 5ml = 4.5ml bd
Example (BSA) - Aciclovir [Refer to BNF]
A 9-year-old child with a BSA calculated at 1.2m2 requires an I/V infusion of aciclovir. What is the 8-hourly dose?
1.2m2 x 500mg/m2 = 600mg every 8 hours
Refer to BNF: Dopamine Hydrochloride
- What is the maximum dose of dopamine that can be given to a 70kg adult patient?
-Dopamine infusion vials contain 200mg/5ml. What volume of dopamine should be used to provide a 6-hour infusion?
a. 70 x 5mcg = 350mcg/min
b. 350mcg x 60 (minutes) x 6 (hours) = 126,000 mcg = 126mg
Need: (126mg/200mg) x 5ml = 3.15ml
A 75kg patient requires an atenolol intravenous infusion after admission for an arrythmia [Refer to BNF Hypertension]
- What dose of atenolol is required initially?
- Atenolol is available as 5mg/10ml solution for injection ampoules. How much should be added to the infusion solution for a single dose?
- 75kg x 150mcg = 11,250mcg (11.25mg) over 20 minutes
- (11.25mg/5mg) x 10ml = 22.5ml
