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
Why is a baseline platelet count taken before starting heparin therapy?
ASo a later fall from heparin-induced thrombocytopenia is detected
BSo that the INR can be calculated from the platelet count later
CBecause heparin is given at a dose based on the platelet count
DBecause heparin increases the platelet count to dangerous levels
2.Lab values & electrolytesHard
A patient on an IV insulin infusion has a blood glucose of 65 mg/dL (3.6 mmol/L). What is the best action?
AContinue at the same rate and recheck in four hours
BFollow the protocol for low glucose and inform the provider
CGive oral potassium to protect the heart
DStop the infusion and leave the glucose recheck until the morning
3.Arterial blood gas interpretationMedium
A practice gas shows PaCO₂ 58 mmHg (7.7 kPa). Use the rule that in chronic respiratory acidosis HCO₃⁻ rises by 3.5 mmol/L for every 10 mmHg that PaCO₂ is above 40, starting from HCO₃⁻ 24 mmol/L, to find the expected HCO₃⁻.
Practice values: Na⁺ 146, Cl⁻ 99 and HCO₃⁻ 18 mmol/L. Calculate the delta ratio (AG − 12)/(24 − HCO₃⁻), using AG = Na⁺ − (Cl⁻ + HCO₃⁻). Give two decimals.
Na⁺ 146 mmol/LCl⁻ 99 mmol/LHCO₃⁻ 18 mmol/L
delta ratio =
5.Clinical pharmacokineticsMedium
Practice exercise (made-up values, not clinical guidance). After an IV dose of vancomycin, the level is 40 mg/L at 1 h and 20 mg/L at 9 h. Assume first-order elimination. Find the half-life t½.
C1 = 40 mg/L (1 h)C2 = 20 mg/L (9 h)
t½ = h
6.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A 55 kg patient takes oral aminophylline (S = 0.8, F = 1) every 12 h. The theophylline clearance is 0.05 L/kg/h. Each dose is 400 mg of aminophylline. Find the average steady-state level Css,avg.
A patient's abdomen is rigid and board-like, and they lie very still because movement worsens the pain. What does this suggest?
AUrinary tract infection
BIndigestion
CConstipation
DPeritonitis
8.Clinical nursingHard
A patient with a head injury shows rising blood pressure, a falling heart rate and irregular breathing. This suggests:
AHypovolaemic shock from hidden internal bleeding
BA panic attack
CSepsis
DRaised intracranial pressure (Cushing's triad)
3Solutions
1.Lab values & electrolytes
Answer: A · So a later fall from heparin-induced thrombocytopenia is detected
Why this is the answer
Heparin-induced thrombocytopenia is diagnosed partly by a fall of about 50% or more from the baseline count, usually 5–14 days after starting. A baseline count and regular checks make this possible.Checked against:Heparin-Induced Thrombocytopenia · StatPearls (NCBI Bookshelf) (2023)
Answer
A · So a later fall from heparin-induced thrombocytopenia is detected
2.Lab values & electrolytes
Answer: B · Follow the protocol for low glucose and inform the provider
Why this is the answer
A glucose below 70 mg/dL on an insulin infusion is hypoglycemia. The nurse follows the hospital’s protocol, which typically stops or reduces the insulin and gives glucose, rechecks often and informs the provider.Checked against:Low blood sugar · MedlinePlus (NIH) (2026)
Answer
B · Follow the protocol for low glucose and inform the provider
3.Arterial blood gas interpretation
Answer: HCO₃⁻ = 30.3 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
|58 − 40| = 18 mmHg → 1.8 × 10 mmHg
Expected HCO₃⁻
HCO₃⁻ = 24 + 3.5·1.8 = 30.3 mmol/L
Answer
HCO₃⁻ = 30.3 mmol/L
4.Arterial blood gas interpretation
Answer: delta ratio = 2.833
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.
Anion gap
AG = 146 − (99 + 18) = 29
Delta ratio
(29 − 12)/(24 − 18) = 17/6 = 2.833
Answer
delta ratio = 2.833
Above 2: an added metabolic alkalosis.
5.Clinical pharmacokinetics
Answer: t½ = 8 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.
Elimination rate constant
k = ln(40/20)/8 = 0.6931/8 = 0.08664 h⁻¹
Half-life
t½ = 0.693/0.08664 = 8 h
Answer
t½ = 8 h
6.Clinical pharmacokinetics
Answer: Css,avg = 9.697 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.
Peritonitis, often from perforation, causes guarding, rigidity and pain worsened by movement. It is a surgical emergency.
Answer
D · Peritonitis
8.Clinical nursing
Answer: D · Raised intracranial pressure (Cushing's triad)
Why this is the answer
Cushing's triad (hypertension with widened pulse pressure, bradycardia and irregular respiration) is a late sign of raised ICP and needs emergency treatment.
Answer
D · Raised intracranial pressure (Cushing's triad)