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
When should blood cultures be taken for a patient with suspected sepsis?
AAfter the first three doses of antibiotics
BBefore the first antibiotic dose, without delaying it much
COnly if the fever lasts more than three days
DAt any time, since antibiotics do not affect the result
2.Lab values & electrolytesHard
A lithium level of 1.0 mEq/L was drawn 2 hours after the patient’s morning dose, and the prescriber plans to raise the dose. What should the nurse point out?
ALithium levels can be drawn at any time of day without affecting the result
BThe level is toxic, so lithium should be stopped for good
CThe sample was taken too soon after the dose, so it is not a valid level
DThe level is too low, so a large increase is clearly safe
3.Arterial blood gas interpretationMedium
A practice arterial blood gas shows pH 7.53, PaCO₂ 51 mmHg (6.8 kPa) and HCO₃⁻ 41 mmol/L. The primary disorder is metabolic alkalosis. How far is it compensated? Click your answer.
pH 7.53PaCO₂ 51 mmHg (6.8 kPa)HCO₃⁻ 41 mmol/L
1uncompensated
2partially compensated
3fully compensated
4.Arterial blood gas interpretationHard
At sea level, a practice gas taken on 35% oxygen shows PaO₂ 89 mmHg (11.9 kPa) and PaCO₂ 38 mmHg (5.1 kPa). Use PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 to find the A–a gradient.
Practice exercise (made-up values, not clinical guidance). Vancomycin is given as a continuous infusion to a patient whose vancomycin clearance is 80 mL/min. What infusion rate R in mg/h gives a steady-state level of 25 mg/L?
CL = 80 mL/minCss = 25 mg/L
R = mg/h
6.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A patient's gentamicin half-life is 2.5 h. The target is a peak of 7 mg/L and a trough of 1 mg/L. Assuming rapid IV doses and first-order elimination, what dosing interval τ lets the level fall from the peak to the trough? Round to one decimal place.
t½ = 2.5 hCpeak = 7 mg/LCtrough = 1 mg/L
τ = h
7.Clinical nursingMedium
A patient is newly confused, has a respiratory rate of 24/min and a systolic blood pressure of 95 mmHg. What should you suspect first?
AAnxiety
BAlcohol intoxication
CNormal postoperative recovery
DSepsis
8.Clinical nursingHard
A patient with small cell lung cancer has hyponatraemia, concentrated urine and no signs of dehydration. Which condition and first measure fit best?
ADiabetes insipidus, managed with extra fluids
BSIADH, often managed first with fluid restriction
CDehydration, managed with an IV fluid bolus
DCushing's syndrome, managed with potassium
3Solutions
1.Lab values & electrolytes
Answer: B · Before the first antibiotic dose, without delaying it much
Why this is the answer
Blood cultures are taken before antibiotics, because even one dose can prevent bacteria from growing and hide the cause. Antibiotics should still be started quickly, ideally within an hour.Checked against:Sepsis · MedlinePlus (NIH) (2024)
Answer
B · Before the first antibiotic dose, without delaying it much
2.Lab values & electrolytes
Answer: C · The sample was taken too soon after the dose, so it is not a valid level
Why this is the answer
Lithium levels are standardized at about 12 hours after the last dose, usually just before the morning dose. A sample 2 hours after a dose catches the absorption peak and is not comparable with the target range, so the dose should not be changed on it.
Answer
C · The sample was taken too soon after the dose, so it is not a valid level
3.Arterial blood gas interpretation
Answer: partially compensated
Reading a blood gas (ROME): first the pH: below 7.35 is acidaemia, above 7.45 alkalaemia. Then find the value that explains it. PaCO₂ (normal 35–45 mmHg, 4.7–6.0 kPa) is the respiratory part and moves Opposite to the pH in a respiratory disorder; HCO₃⁻ (normal 22–26 mmol/L) is the metabolic part and moves in the same direction as the pH (Respiratory Opposite, Metabolic Equal). The other value shows the compensation: normal means uncompensated; abnormal in the direction that pulls the pH back while the pH is still abnormal means partially compensated; a normal pH with both values abnormal means fully compensated. Ranges differ slightly between laboratories; these are practice values.
ROME, value by value
pH 7.53: alkalaemia (above 7.45)
PaCO₂ 51 mmHg: high (35–45)
HCO₃⁻ 41 mmol/L: high (22–26)
Compensation
partially compensated
Answer
partially compensated
4.Arterial blood gas interpretation
Answer: A–a gradient = 113 mmHg
Derived values: calculated serum osmolality is 2·Na⁺ + glucose + urea with all values in mmol/L (2·Na⁺ + glucose/18 + BUN/2.8 with glucose and BUN in mg/dL); normal is about 275–295 mOsm/kg. The P/F ratio is PaO₂ divided by FiO₂ as a fraction. The alveolar oxygen pressure is PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 mmHg at sea level, and the A–a gradient is PAO₂ − PaO₂.
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.
Clearance in L/h
80·60/1000 = 4.8 L/h
Infusion rate
R = 4.8·25 = 120 mg/h
Answer
R = 120 mg/h
6.Clinical pharmacokinetics
Answer: τ = 7 h
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.
Rate constant
k = 0.693/2.5 = 0.2773 h⁻¹
Dosing interval
τ = ln(7/1)/0.2773 = 1.946/0.2773 = 7.018 ≈ 7 h
Answer
τ = 7 h
In practice the interval is rounded to a convenient value such as 8, 12, 24 or 36 h, and the levels are checked again.
7.Clinical nursing
Answer: D · Sepsis
Why this is the answer
These three signs form the qSOFA criteria and suggest a high risk of poor outcome from sepsis. Escalate urgently and start the sepsis pathway.
Answer
D · Sepsis
8.Clinical nursing
Answer: B · SIADH, often managed first with fluid restriction
Why this is the answer
In SIADH, excess ADH makes the kidneys retain water, so blood sodium is diluted while urine is concentrated. Small cell lung cancer is a classic cause; fluid restriction is a common first step.
Answer
B · SIADH, often managed first with fluid restriction