Read the pH: below 7.35 is acidosis, above 7.45 alkalosis.
Find the value that explains it: PaCO₂ moving opposite to the pH is respiratory, HCO₃⁻ moving with the pH is metabolic.
Look at the other value: normal means uncompensated, abnormal in the compensating direction means partial compensation, and a normal pH with both abnormal means full compensation.
In a metabolic acidosis, compare PaCO₂ with Winter’s formula, 1.5·HCO₃⁻ + 8 ± 2, and calculate the anion gap Na⁺ − (Cl⁻ + HCO₃⁻).
Check a high anion gap with the delta ratio and, when albumin is low, with the corrected gap.
Clinical pharmacokinetics
Rate constant and half-life
k = ln 2/t½ = 0.693/t½
First-order decay
C = C₀·e−kt = C₀·(1/2)t/t½
Two levels
k = ln(C₁/C₂)/Δt
Volume and clearance
Vd = dose/C₀, CL = k·Vd
Loading dose
LD = Vd·C/(S·F)
Maintenance rate
R = CL·Css/(S·F)
Average steady state
Css,avg = S·F·D/(CL·τ)
Steady state
1 − (1/2)ⁿ after n half-lives; ≈ 97% after 5
Infusion
C = (R/CL)(1 − e−kt)
Interval and dose from peak and trough
τ = ln(Cpeak/Ctrough)/k, D = Vd·(Cpeak − Ctrough)
Cockcroft–Gault
CrCl = (140 − age) × kg/(72 × SCr mg/dL), × 0.85 for women
Pick the relation: C = C₀·e−kt, LD = Vd·C/(S·F), maintenance rate = CL·Css/(S·F), τ = ln(Cpeak/Ctrough)/k.
For kidney function, estimate CrCl with Cockcroft–Gault first, then scale the dose or the interval.
Check the result: levels fall by half every half-life, and steady state takes about five half-lives.
2Practice problems
1.Lab values & electrolytesMedium
A stable adult who is not bleeding receives one unit of packed red cells. By about how much is the hemoglobin expected to rise?
AAbout 0.1 g/dL (1 g/L)
BAbout 1 g/dL (10 g/L)
CAbout 5 g/dL (50 g/L)
DAbout 3 g/dL (30 g/L)
2.Lab values & electrolytesHard
A patient with diabetes had a glucose of 58 mg/dL (3.2 mmol/L), took 15 g of fast-acting carbohydrate and, 15 minutes later, the glucose is 64 mg/dL (3.6 mmol/L). The patient is alert. What should the nurse do next?
AGive another 15 g of fast carbohydrate and recheck
BGive a long-acting insulin dose to stabilize it
CWait until the next meal before giving anything
DGive a protein snack only and recheck tomorrow
3.Arterial blood gas interpretationMedium
A practice gas shows PaCO₂ 21 mmHg (2.8 kPa). Use the rule that in acute respiratory alkalosis HCO₃⁻ falls by 2 mmol/L for every 10 mmHg that PaCO₂ is below 40, starting from HCO₃⁻ 24 mmol/L, to find the expected HCO₃⁻.
A practice gas shows a respiratory acidosis: pH 7.29, PaCO₂ 65 mmHg (8.7 kPa), HCO₃⁻ 30 mmol/L. Use the rules ‘HCO₃⁻ rises 1 mmol/L per 10 mmHg (acute) or 3.5 mmol/L per 10 mmHg (chronic)’ to classify it. Click your answer.
pH 7.29PaCO₂ 65 mmHg (8.7 kPa)HCO₃⁻ 30 mmol/L
1acute
2chronic
3acute on chronic
5.Clinical pharmacokineticsMedium
Practice exercise (made-up values, not clinical guidance). A patient receives an IV bolus of 230 mg of tobramycin. The level back-extrapolated to time zero is 8 mg/L and the half-life is 3 h. Find the clearance CL in L/h.
D = 230 mgC₀ = 8 mg/Lt½ = 3 h
CL = L/h
6.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A patient receives vancomycin IV every 12 h; the vancomycin clearance is 4 L/h. Each dose is 750 mg of vancomycin. Find the average steady-state level Css,avg.
CL = 4 L/hτ = 12 hS = 1F = 1D = 750 mg
Css,avg = mg/L
7.Clinical nursingMedium
Which assessment best detects compartment syndrome after a fractured leg is put in a cast?
AA strong pulse in the foot
BMild itching under the cast
CA warm, pink foot
DPain out of proportion to the injury, especially on passive stretch
8.Clinical nursingHard
A patient with metastatic breast cancer is confused and constipated, with a corrected calcium of 3.3 mmol/L (about 13.2 mg/dL). What is usually the first treatment?
AIV fluid rehydration, followed by a bisphosphonate
BOral calcium supplements and vitamin D
CA high-calcium diet
DStrict fluid restriction to protect the kidneys
3Solutions
1.Lab values & electrolytes
Answer: B · About 1 g/dL (10 g/L)
Why this is the answer
In an average-sized adult without ongoing bleeding or hemolysis, one unit of red cells raises the hemoglobin by about 1 g/dL (and the hematocrit by about 3%). A smaller rise suggests ongoing blood loss or red cell destruction.Checked against:Blood Transfusion · StatPearls (NCBI Bookshelf) (2026)
Answer
B · About 1 g/dL (10 g/L)
2.Lab values & electrolytes
Answer: A · Give another 15 g of fast carbohydrate and recheck
Why this is the answer
The "15-15 rule" is repeated until the glucose is at least 70 mg/dL (3.9 mmol/L); UK guidance uses 4.0 mmol/L and 15–20 g of carbohydrate. Then a snack or meal with complex carbohydrate and protein is given if the next meal is not soon, to prevent recurrence.
Answer
A · Give another 15 g of fast carbohydrate and recheck
3.Arterial blood gas interpretation
Answer: HCO₃⁻ = 20.2 mmol/L
Expected compensation: in metabolic acidosis Winter’s formula predicts PaCO₂ = 1.5·HCO₃⁻ + 8 ± 2 mmHg; a measured value above that range points to an additional respiratory acidosis, below it to an additional respiratory alkalosis. The anion gap AG = Na⁺ − (Cl⁻ + HCO₃⁻), normally about 8–12 mmol/L, separates high-gap from normal-gap metabolic acidosis; low albumin hides a high gap (add 2.5 per g/dL that albumin is below 4.0). The delta ratio (AG − 12)/(24 − HCO₃⁻) between about 0.8 and 2 fits a pure high-gap acidosis (some texts use 1 instead of 0.8), below that an added normal-gap acidosis, and above 2 an added metabolic alkalosis.
Change in PaCO₂
|21 − 40| = 19 mmHg → 1.9 × 10 mmHg
Expected HCO₃⁻
HCO₃⁻ = 24 − 2·1.9 = 20.2 mmol/L
Answer
HCO₃⁻ = 20.2 mmol/L
4.Arterial blood gas interpretation
Answer: acute on chronic
Expected compensation: in metabolic acidosis Winter’s formula predicts PaCO₂ = 1.5·HCO₃⁻ + 8 ± 2 mmHg; a measured value above that range points to an additional respiratory acidosis, below it to an additional respiratory alkalosis. The anion gap AG = Na⁺ − (Cl⁻ + HCO₃⁻), normally about 8–12 mmol/L, separates high-gap from normal-gap metabolic acidosis; low albumin hides a high gap (add 2.5 per g/dL that albumin is below 4.0). The delta ratio (AG − 12)/(24 − HCO₃⁻) between about 0.8 and 2 fits a pure high-gap acidosis (some texts use 1 instead of 0.8), below that an added normal-gap acidosis, and above 2 an added metabolic alkalosis.
Expected HCO₃⁻
acute: 24 + 1·2.5 = 26.5 mmol/L
chronic: 24 + 3.5·2.5 = 32.75 mmol/L
Compare
measured: 30 mmol/L → acute on chronic
Answer
acute on chronic
5.Clinical pharmacokinetics
Answer: CL = 6.643 L/h
Clearance and volume: at steady state the dosing rate equals the elimination rate, so the maintenance rate = CL × Css. A loading dose is LD = Vd × C/(S × F), with S the salt factor (fraction of active drug in the salt) and F the bioavailability (1 for IV). From two levels, k = ln(C₁/C₂)/Δt; for an IV bolus Vd = dose/C₀ and CL = k × Vd. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Volume of distribution
Vd = 230/8 = 28.75 L
Rate constant
k = 0.693/3 = 0.231 h⁻¹
Clearance
CL = 0.231·28.75 = 6.643 L/h
Answer
CL = 6.643 L/h
6.Clinical pharmacokinetics
Answer: Css,avg = 15.63 mg/L
Designing a regimen: with rapid IV doses the level falls from peak to trough during the interval, so τ = ln(Cpeak/Ctrough)/k and the dose that restores the peak is Vd × (Cpeak − Ctrough). The average steady-state level is Css,avg = S·F·dose/(CL·τ). An infusion rises as C = (R/CL)(1 − e−kt). For a drug cleared by the kidneys, the dose is scaled with the creatinine clearance. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Answer: D · Pain out of proportion to the injury, especially on passive stretch
Why this is the answer
Increasing pain that is not relieved by analgesia and worsens with passive stretching is the earliest sign. Pallor, numbness and absent pulses are late signs.
Answer
D · Pain out of proportion to the injury, especially on passive stretch
8.Clinical nursing
Answer: A · IV fluid rehydration, followed by a bisphosphonate
Why this is the answer
Hypercalcaemia of malignancy causes dehydration, so IV fluids are given first, followed by a bisphosphonate to reduce bone resorption. Calcium, renal function and fluid balance are monitored.
Answer
A · IV fluid rehydration, followed by a bisphosphonate