Calculations II Part 2
How many grams of NaCl are in 250 mL of NS? (Answer must be numeric; no units or commas; include a leading zero when answer is less than 1.)
2.25 g (0.9 g/100 mL) = (x g/250 mL) = 2.25 g
What is the percentage strength of neomycin in the following prescription? (Answer must be numeric; no units or commas; include a leading zero when answer is less than 1.) Rx: Neomycin (5%) cream 30 g Polymyxin B 20 g Hydrocortisone 10 g
2.5% Neomycin 5% = 5 g/100 g 5 g/100 g x 30 g = 1.5 g 1.5 ÷ 60 = 0.025 0.025 x 100 = 2.5%
A pharmacist has prepared a PN that contains 600 grams of dextrose. How many calories are provided by the dextrose? (Answer must be numeric; no units or commas.)
2040 kcal D = 3.4 kcal/gram 3.4 kcal x 600 grams = 2040 kcal
How many calories are provided by 275 mL of 50% dextrose in water? (Answer must be numeric; no units or commas; round final answer to the nearest TENTH.)
467.7 kcal 50 g/100 mL = x g/275 mL = 137.5 g D = 3.4 kcal x 137.5 g = 467.5 kcal
What is the pH of a solution containing 0.2 mole of a weak acid and 1 mole of its salt? (pKa of the acid = 5.35). (Answer must be numeric; no units or commas; include a leading zero when answer is less than 1; round final answer to the nearest HUNDREDTH.)
6.05 pH (weak acid) = pKa + log[salt/acid] 5.35 + log[1 mole/0.2 mole] = 6.05
The "E value" for tobramycin is 0.07. A prescription is received for 10 mL of a 1% tobramycin eye drop solution. How many milligrams of NaCl need to be added to make the eye drop isotonic? (Answer must be numeric; no units or commas; include a leading zero when answer is less than 1.)
83 mg 0.9 g/100 mL = x g/10 mL = 0.09 g → 90 mg Determine amount of sodium chloride represented from tobramycin 1 g/100 mL = x g/10 mL = 0.1 g or 100 mg 100 mg x 0.07 ("E" value) = 7 mg of NaCl 90 mg - 7 mg = 83 mg
An elderly male is hospitalized with sepsis. He is 6 feet tall and 143 pounds. Select the correct BMI for this patient and the corresponding classification: A) 18.2, underweight B) 19.4, underweight C) 19.4, obese D) 18.2, overweight E) 19.4, normal weight
E) 19.4, normal weight BMI = [(wt (lb)) ÷ (Ht (in)²] x 703 [143 ÷ 72²] x 703 = 19.4 < 18.5 = Underweight 18.5 - 24.9 = Normal weight 25 - 29.9 = Overweight ≥ 30 = Obese
An ear drop contains 18 mg of lidocaine in each milliliter of solution. Calculate the percentage strength (w/v) of lidocaine. (Answer must be numeric; no units or commas; include a leading zero when answer is less than 1.)
1.8% (0.018 g/1 mL) = (x g/100 mL) = 1.8%
CB, a 63 year old male, is receiving 1,150 mL of D30W, 860 mL of Aminosyn 8.5%, and 340 mL of Intralipid 10% in his PN therapy. What percentage of the non-protein calories are represented by dextrose? (Answer must be numeric; no units or commas; round to the nearest WHOLE number.)
76% 30 g/100 mL = x g/1150 mL = 345 g D = 3.4 kcal x 345 g = 1173 kcal L 10% = 1.1 kcal x 340 mL = 374 kcal 1173 kcal D + 374 kcal L10% = 1547 kcal of non-protien calories 1173 kcal D ÷ 1547 kcal total = 76%
How many moles are equivalent to 290 mg of aluminum hydroxide? (M.W. = 78). (Answer must be numeric; no units or commas; include a leading zero when answer is less than 1; round final answer to three decimal places.)
0.004 mols mols = g/MW 290 mg → 0.29 g 0.29/78 = 0.004 mols
A dexamethasone elixir contains 0.5 mg dexamethasone per 5 mL. What is the percentage strength (w/v) of the dexamethasone elixir in this prescription? (Answer must be numeric; no units or commas; include a leading zero when answer is less than 1.)
0.01% 0.5 mg = 0.0005 g (0.0005 g/5 mL) = (x g/100 mL) = 0.01%
The pharmacy has an order for 10 mL of tobramycin 1% ophthalmic solution. The pharmacy has in stock tobramycin 40 mg/mL solution. Tobramycin has a M.W. of 468 and does not dissociate. NaCl has a M.W. of 58.5 and a dissociation factor of 1.8. What is the equivalent value (the "E value") of tobramycin? (Answer must be numeric; no units or commas; include a leading zero when answer is less than 1; round final answer to two decimal places.)
0.07 E = [(58.5)x(i)] ÷ [(MW)x(1.8)] Tobramycin does not dissociate so i = 1 (58.5 x 1) ÷ (468 x 1.8) = 0.07
A pharmacy technician added 10 mL of a 20% (w/v) solution of potassium chloride to a 500 mL bag of normal saline. What is the percentage strength of potassium chloride in the bag? (Answer must be numeric; no units or commas; include a leading zero when answer is less than 1; round final answer to the nearest HUNDREDTH.)
0.39% 20 g/100 mL = x g/10 mL = 2 g 10 mL + 500 mL = 510 mL 2 g/510 mL = x g/100 mL = 0.39%
A prefilled syringe contains 50 mg of phenylephrine hydrochloride per 5 mL of injection. Express the percentage concentration (w/v) of phenylephrine in the injection. (Answer must be numeric; no units or commas; include a leading zero when answer is less than 1.)
1% 50 mg → 0.05 g 0.05 g/5 mL = x g/100 mL = 1%
How many milligrams of sodium hydroxide (M.W. = 40) are represented by 0.25 mmol? (Answer must be numeric; no units or commas; include a leading zero when answer is less than 1.)
10 mg mmols = mg/MW 0.25 mmols = x mg/40 10 mmols = x mg = 10 mg
What is the pH of a solution prepared to be 0.4 M ammonia and 0.04 M ammonium chloride (pKb for ammonia = 4.76)? (Answer must be numeric; no units or commas; include a leading zero when answer is less than 1; round final answer to the nearest two decimal places.)
10.24 pH(weak base) when pKa provided = pKa + log[base/salt] pH(weak base) when pKb provided = (pKw* - pKb) + log[base/salt] (14-4.76) + log[0.4/0.04] = 10.24 *pKw always equals 14
What is the osmolarity, in mOsm/L, of 3% NaCl? (M.W. = 58.5). (Answer must be numeric; no units or commas; round final answer to the nearest WHOLE number.)
1026 mOsm/L mOsm/L = [(wt of substance (g/L))÷(MW)] x # of particles x 1000 (3 g/100 mL) = (x g/1000 mL) = 30 g (30 g ÷ 58.5) x 2 x 1000 = 1026 mOsm/L
VH is a 37 year old female who is receiving 334 grams of dextrose, 87 grams of amino acids, and 310 mL of 10% lipids via her PN therapy. What percentage of calories is provided by the protein content? (Answer must be numeric; no units or commas; round final answer to the nearest WHOLE number.)
19% D = 3.4 kcal/gram AA = 4 kcal/gram = protein L 10% = 1.1 kcal/mL D = 3.4 kcal x 334 grams = 1135.6 kcal AA = 4 kcal x 87 grams = 348 kcal L 10% = 1.1 kcal x 310 mL = 341 kcal 1824.6 total kcal 348 kcal AA ÷ 1824.6 kcal total = 19%
An 80 year-old male has a severe diabetic foot infection. He will be started on broad spectrum empiric therapy including piperacillin/tazobactam (Zosyn). The recommended renal dose adjustments for Zosyn and the patient's labs/demographic data are provided below. CrCl (mL/min) Zosyn Dose > 40 3.375 g IV Q6H 20 - 40 2.25 g IV Q6H < 20 2.25 g IV Q8H Physical Exam / Vitals: Height: 5'3" Weight: 118 pounds BP: 153/72 mmHg HR: 62 BPM RR: 14 BPM Temp: 101.3°F Pain: 9/10 CV: Regular Extremities: Severe bilateral lower extremity wounds. Wounds are open with purulent drainage. Two small wounds on left extremity appear to be necrotic. Labs: Na (mEq/L) = 137 (135 - 145) K (mEq/L) = 4.8 (3.5 - 5) Cl (mEq/L) = 101 (95 - 103) HCO3 (mEq/L) = 26 (24 - 30) BUN (mg/dL) = 22 (7 - 20) SCr (mg/dL) = 1.3 (0.6 - 1.3) Glucose (mg/dL) = 279 (100 - 125) Ca (mg/dL) = 9.2 (8.5 - 10.5) Mg (mEq/L) = 1.5 (1.3 - 2.1) PO4 (mg/dL) = 2.9 (2.3 - 4.7) WBC (cells/mm3) = 11.2 (4 - 11 x 103) Hgb (g/dL) = 14.5 (13.5 - 18 male) Hct (%) = 43.4 (38 - 50 male) Plt (cells/mm3) = 342 (150 - 450 x 103) AST (IU/L) = 25 (10 - 40) ALT (IU/L) = 12 (10 - 40) Albumin (g/dL) = 3.9 (3.5 - 5) A1C (%) = 11.8 Question: What is the correct starting dose of Zosyn for this patient?
2.25 g IV Q6H CrCl = [(140 - age) ÷ (72 x SCr)] x wt in kg [(140 - 80) ÷ (72 x 1.3)] x 53.64 = 34.38
The pharmacy receives the following PN order. What percentage of the total calories are represented by the protein component? (Answer must be numeric; no units or commas; round final answer to the nearest WHOLE number.) Item/Quantities: Dextrose 270 g Amino acids 60 g Sodium chloride 38 mEq Sodium acetate 16 mEq Potassium 40 mEq Magnesium sulfate 10 mEq Phosphate 21 mmol Calcium 4.45 mEq MVI-12 5 mL Trace elements 1 mL Vitamin K-1 0.5 mg Famotidine 10 mg Regular insulin 40 units Sterile water qs ad 980 mL
21% D = (3.4 kcal/gram) x 270 gram = 918 kcal AA = 4 kcal/gram x 60 gram = 240 kcal 918 kcal + 240 kcal = 1158 kcal total 240 kcal AA ÷ 1158 kcal total = 21%
A patient is to receive 10 mEq of calcium. The pharmacy has calcium gluconate 10% in stock, which contains 0.465 mEq/mL of calcium. How many milliliters of calcium gluconate are required? (Answer must be numeric; no units or commas; round final answer to the nearest WHOLE number.)
22 mL Patient is receiving 10 mEq of calcium Calcium gluconate contains 0.465 mEq/mL of calcium 10 mEq ÷ 0.465 mEq/mL = 22 mL
A patient is to receive 11 mEq of calcium. The pharmacy has calcium gluconate 10% in stock which provides 0.465 mEq/mL. How many mL of calcium gluconate should be added to the PN? (Answer must be numeric; no units or commas; round final answer to the nearest TENTH.)
23.7 mL 0.465 mEq/1 mL = 11 mEq/x mL = 23.7 mL
The pharmacy receives the following PN order. Calculate the mL of dextrose 70% that should be added to the PN. (Answer must be numeric; no units or commas; round final answer to the nearest WHOLE number.) Item/Quantities: Dextrose 270 g Amino acids 60 g Sodium chloride 38 mEq Sodium acetate 16 mEq Potassium 40 mEq Magnesium sulfate 10 mEq Phosphate 21 mmol Calcium 4.45 mEq MVI-12 5 mL Trace elements 1 mL Vitamin K-1 0.5 mg Famotidine 10 mg Regular insulin 40 units Sterile water qs ad 980 mL
386 mL 70 g/100 mL = 270 g/x mL = 386 mL
A pharmacist is approached by a physician for help writing a parenteral nutrition order. The patient is currently receiving a 2-in-1 formula consisting of 425 grams of dextrose and 110 grams of protein. Dietary Progress Note: "Patient needs 2,400 calories per day. Recommend 10% Intralipid infusion to provide the remaining calories". Hospital policy is to infuse the daily lipid requirement over 12 hours to reduce infection risk. What rate (mL/hr) should the pharmacist recommend for the Intralipid to provide the necessary calories? (Answer must be numeric; no units or commas; round to the nearest WHOLE number.)
39 mL/hour D = 3.4 kcal x 425 grams = 1445 kcal AA = 4 kcal x 110 grams = 440 kcal 1445 + 440 = 1885 kcal 2400 kcal - 1885 kcal = 515 kcal remaining L 10% = 1.1 kcal/mL = 515 kcal/1.1 kcal/m/L = 468.18 mL from Lipids 468.18 mL ÷ 12 hrs = 39 mL/hour
A hospital pharmacist receives a prescription for 3% saline for a patient in the Neuro ICU. The premixed 3% saline bags that the pharmacy normally stocks are on backorder. How many milliequivalents of 23.4% NaCl will need to be added to a 1 liter bag of normal saline to prepare 3% saline for this patient? (MW of Na = 23; MW of Cl = 35.5). (Answer must be numeric; no units or commas; round final answer to the nearest TENTH.)
411.8 mEq 23.4 2.1 3 0.9 20.4 (2.1 parts of 23.4% / 20.4 parts of 0.9%) = (X mL of 23.4% / 1000 mL of 0.9%) x = 102.941 mL of 23.4% 23.4% = 23.4 g/100 mL 23.4 g/100 mL x 102.941 mL = 24.088 g 24.088 = 24088 mg mEq = (mg x valence) ÷ (MW) (24088 mg x 1) ÷ (58.5) = 411.8 mEq
The pharmacy receives the following PN order. The PN calls for 21 mmol of phosphate and 4.45 mEq of calcium in a total volume of 980 mL. There are 2 mEq of phosphate/mmol. Calculate the total milliequivalents (mEq) of calcium and phosphorus in the PN. (Answer must be numeric; no units or commas; round the final answer to the nearest WHOLE number.)
46 mEq 2 mEq x 21 mmol = 42 mEq PO₄ 42 mEq PO₄ + 4.45 mEq Ca = 46 mEq
A PN contains 7 mL of potassium phosphate (each mL contains 3 mmol of phosphate and 4.4 mEq of potassium). The daily potassium requirement is 42 mEq. How many milliliters of potassium chloride (2 mEq/mL) should be added to the PN? (Answer must be numeric; no units or commas.)
5.6 mL 7 mL x 4.4 mEq = 30.8 mEq of K from KPO₄ 42mEq - 30.8 mEq = 11.2 mEq of K remaining to meet the daily K requirement 11.2 mEq ÷ 2 mEq/mL KCl = 5.6 mL
What is the osmolarity, in mOsm/L, of D10W? (M.W. = 198). (Answer must be numeric; no units or commas; round final answer to the nearest WHOLE number.)
505 mOsm/L (10 g/100 mL) = (x g/1000 mL) = 100 g (100 g ÷ 198) x 1 x 1000 = 505 mOsm/L
The pharmacy receives the following PN order. How many milliliters of potassium phosphate (each mL contains 3 mmol of phosphate and 4.4 mEq of potassium) should be added to the PN to fulfill the phosphate requirements? (Answer must be numeric; no units or commas.) Item/Quantities: Dextrose 270 g Amino acids 60 g Sodium chloride 38 mEq Sodium acetate 16 mEq Potassium 40 mEq Magnesium sulfate 10 mEq Phosphate 21 mmol Calcium 4.45 mEq MVI-12 5 mL Trace elements 1 mL Vitamin K-1 0.5 mg Famotidine 10 mg Regular insulin 40 units Sterile water qs ad 980 mL
7 mL KPO₄ = 3 mmol/mL of PO₄ & 40 mmol/mL of K Patient requires 21 mmol of PO₄ 21 mmol ÷ 3 mmol/mL = 7 mL
The pharmacist is going to add 60 mEq of sodium to the PN; half will be given as sodium acetate (2 mEq/mL) and half as sodium chloride (4 mEq/mL). How many milliliters of sodium chloride will be needed? (Answer must be numeric; no units or commas.)
7.5 mL 60 mEq ÷ 2 = 30 mEq 30 mEq ÷ 4 mEq/mL = 7.5 mL
The pharmacy receives the following PN order. How many milliliters of sodium acetate 16.4% (2 mEq/mL) should be added to the PN? (Answer must be numeric; no units or commas.) Item/Quantities: Dextrose 270 g Amino acids 60 g Sodium chloride 38 mEq Sodium acetate 16 mEq Potassium 40 mEq Magnesium sulfate 10 mEq Phosphate 21 mmol Calcium 4.45 mEq MVI-12 5 mL Trace elements 1 mL Vitamin K-1 0.5 mg Famotidine 10 mg Regular insulin 40 units Sterile water qs ad 980 mL
8 mL Sodium acetate 2 mEq/mL PN requires 16 mEq 16 ÷ 2 = 8 mL
If a solution contains 20 g of glycerol and 5 g of codeine, what is the glycerol percentage strength (w/w) of the solution? (Answer must be numeric; no units or commas; include a leading zero when answer is less than 1.)
80% 20 g + 5 g = 25 g 20 g/25 g = x g/100 g = 80% 25 g
A patient requires 400 grams of dextrose in their PN bag. If the pharmacist is using D50W, how many milliliters of D50W will be needed to provide the 400 grams? (Answer must be numeric; no units or commas.)
800 mL 50 g/100 mL = 400 g/x mL = 800 mL
How many milligrams of NaCl are in a 10 mL vial of NS? (Answer must be numeric; no units or commas; include a leading zero when answer is less than 1.)
90 mg NS = 0.9% = 0.9 g/100mL (0.9 g/100 mL) = (x g/10 mL) x = 0.09 g → 90 mg
Which of the following are causes of elevated anion gap metabolic acidosis? (Select ALL that apply.) A) Diabetic ketoacidosis B) Salicylate toxicity C) Opioid intoxication D) Diarrhea E) Lactic acidosis
A) Diabetic ketoacidosis B) Salicylate toxicity E) Lactic acidosis
An elderly male is admitted to the hospital after a motor vehicle accident. He suffered a head injury and is in the ICU. An ABG is obtained and the results are as follows: 6.89/45/82/19/98. What acid base disorder does this patient have? A) Metabolic acidosis B) Metabolic alkalosis C) Respiratory acidosis D) Respiratory alkalosis
A) Metabolic acidosis
The Cockcroft-Gault equation is commonly used by pharmacists to estimate renal clearance. This equation takes into consideration each of the following parameters except: A) Age B) Height C) Weight D) Sex E) Serum creatinine
B) Height CrCl = [(140 - age) ÷ (72 x SCr)] x wt in kg (x 0.85 if female)
The pharmacist receives a prescription for "Cefaclor 500 mg #30, Sig: i cap po q 8 hrs ATC." Choose the correct wording for the prescription label. A) Take 1 capsule by mouth 8 hours after therapeutic concentration is reached. B) Take 1 capsule by mouth every 8 hours around the clock. C) Take 1 capsule by mouth every 8 hours after each meal. D) Take 1 capsule by mouth every 8 hours after chewing, then swallowing. E) Insert 1 tablet by mouth 8 hours after the cavity is cleared.
B) Take 1 capsule by mouth every 8 hours around the clock.
The pharmacist needs to measure out 35 grams of a 70% powder using the 50% and 90% powders he has in stock. How much of each powder is required? A) 25 grams of the 50% and 10 grams of the 90% B) 12.5 grams of the 50% and 22.5 grams of the 90% C) 17.5 grams of the 50% and 17.5 grams of the 90% D) 20 grams of the 50% and 15 grams of the 90% E) 22 grams of the 50% and 13 grams of the 90%
C) 17.5 grams of the 50% and 17.5 grams of the 90% 90 20 70 50 20 35 grams ÷ 40 parts = 0.875 0.875 x 20 = 17.5
An order is written for 10 mL of a 0.125% bupivacaine injection and 10 mL of morphine injection (1 mg/mL) to be mixed with 250 mL of normal saline. The infusion is to be administered over 3 hours. The IV set delivers 20 drops/mL. What should be the rate of flow in drops/minute to deliver this infusion? A) 20.8 drops/minute B) 16.7 drops/minute C) 30 drops/minute D) 28.6 drops/minute E) 21.7 drops/minute
C) 30 drops/minute 10 mL of 0.125% bupivacaine + 10 mL of morphine + 250 mL normal saline = 270 total mL 20 drops/mL = 270 x 20 = 5400 total drops 3 hrs = 180 mins 5400 drops ÷ 180 mins = 30 drops/min
The pharmacist receives a prescription for "Timoptic 0.25%, Sig: i gtt od qam." Choose the correct wording for the prescription label. A) Place 1 drop in each eye daily in the morning. B) Instill 1 drop in the left eye daily in the morning. C) Place 1 drop in each eye after dinner. D) Place 1 drop in the right eye daily in the morning. E) Instill 1 drop in the right eye daily.
D) Place 1 drop in the right eye daily in the morning.
A patient has the following ABG: pH = 7.5, paCO2 = 25, HCO3 = 24. What is the acid-base disorder present in this patient? A) Metabolic acidosis B) Respiratory acidosis C) Metabolic alkalosis D) Respiratory alkalosis E) This is a normal ABG
D) Respiratory alkalosis An acid-base disorder that leads to a pH > 7.45 it is called an alkalosis. In respiratory alkalosis, the pCO2 is decreased. Refer to the Lab Values & Drug Monitoring chapter for the reference ranges of the ABG components.
If you mix 30 gm 5% lidocaine cream and 90gm of 0.5% hydrocortisone cream, what percent of lidocaine and hydrocortisone do you have as the end product? A) Lidocaine/Hydrocortisone 2%/1.25% B) Lidocaine/Hydrocortisone 0.375%/0.15% C) Lidocaine/Hydrocortisone 1.25 %/ 0.15% D) Lidocaine/Hydrocortisone 2% /0.25% E) Lidocaine/Hydrocortisone 1.25% /0.375%
E) Lidocaine/Hydrocortisone 1.25% /0.375% Lidocaine: 30g x 0.05 = 1.5g. Hydrocortisone: 90g x 0.005 = 0.45g. 90g+30g = 120g. 1.5g/120g = 0.0125 x100 = 1.25% Lidocaine. 0.45g/120g = 0.00375 x 100 = 0.375% Hydrocortisone.
Which statement best describes this patient's hydration status based on the labs provided below: Labs: Na (mEq/L) = 139 (135 - 145) K (mEq/L) = 3.9 (3.5 - 5) Cl (mEq/L) = 99 (95 - 103) HCO3 (mEq/L) = 26 (24 - 30) BUN (mg/dL) = 67 (7 - 20) SCr (mg/dL) = 1.7 (0.6 - 1.3) Glucose (mg/dL) = 128 (100 - 125) Ca (mg/dL) = 9.9 (8.5 - 10.5) Mg (mEq/L) = 1.8 (1.3 - 2.1) PO4 (mg/dL) = 2.6 (2.3 - 4.7) A) The patient appears to be well hydrated based on normal values for Na, K, Ca, Mg and PO4. B) The patient appears to be dehydrated based on the normal values for Na, K, Ca, Mg and PO4. C) The patient appears to be dehydrated based on the Na:Cl ratio. D) The patient appears to be well hydrated based on the BUN:SCr ratio. E) The patient appears to be dehydrated based on the BUN:SCr ratio.
E) The patient appears to be dehydrated based on the BUN:SCr ratio. A patient with a BUN:SCr ratio greater than 20:1 can be considered dehydrated. However many hospitalized patients will have a ratio that indicates mild dehydration (such as 21, or 22). More severe dehydration requires more urgent treatment. 67:1.7 = 39:1 = dehydrated
A patient has the following ABG: pH = 7.6, paCO2 = 60, HCO3 = 32 What is the acid-base disorder present in this patient?
Metabolic Alkalosis pH = 7.6 ↑ = Alkalosis HCO₃ = 32 ↑ = Alkalosis PCO₂ = 60 ↑ = Acidosis Which one matches pH? HCO₃ = Metabolic Alkalosis
