Let's break down the problem step by step: **Given:** - Blood flow rate \( Q = 0.35 \) mL/min/cm³ tissue - \( pO_2 \) of **entering blood** = 95 mmHg - \( pO_2 \) of **exiting blood** = 20 mmHg - **Want:** Oxygen consumption rate in **μM/sec** --- ### **Step 1: Find the amount of O\(_2\) delivered and removed (using pO\(_2\) difference)** We will use the oxygen content difference (not just \( pO_2 \)) to calculate the amount consumed. **Assumption:** Most O\(_2\) in blood is bound to hemoglobin. However, unless hemoglobin content is given, we can do the calculation using **dissolved O\(_2\) only** (if you want the full calculation with Hb, more data is needed). Let's proceed with **dissolved O\(_2\)** (if you need with hemoglobin, please clarify!). The concentration of dissolved O\(_2\) in plasma is: \[ [\mathrm{O}_2]_{\text{dissolved}} = \alpha \cdot pO_2 \] where - \( \alpha \) (solubility coefficient) ≈ **0.0031 mL O\(_2\) / 100 mL blood / mmHg** Thus, - [O\(_2\)] in entering blood: \( 0.0031 \times 95 = 0.2945 \) mL O\(_2\) / 100 mL blood - [O\(_2\)] in exiting blood: \( 0.0031 \times 20 = 0.062 \) mL O\(_2\) / 100 mL blood Difference: \[ \Delta [\mathrm{O}_2] = 0.2945 - 0.062 = 0.2325 \text{ mL O}_2 / 100 \text{ mL blood} \] --- ### **Step 2: Calculate total oxygen extracted per minute per cm³ tissue** Blood flow per minute per cm³ = \( Q = 0.35 \) mL/min/cm³ Per min, O\(_2\) extracted: \[ \text{O}_2\, \text{extracted/min} = Q \times \Delta [\mathrm{O}_2] \] But, units: - Q is in mL blood/min/cm³ - Δ[O2] is in mL O2/100 mL blood So, \[ \text{O}_2\, \text{extracted/min} = 0.35\, \text{mL blood/min/cm}^3 \times 0.2325\, \frac{\text{mL O}_2}{100\, \text{mL blood}} \] \[ = 0.35 \times 0.002325\, \text{mL O}_2 / \text{min} / \text{cm}^3 \] \[ = 0.00081375\, \text{mL O}_2 / \text{min} / \text{cm}^3 \] --- ### **Step 3: Convert mL O\(_2\) to μmol O\(_2\)** - 1 mole of gas at STP = **22.4 L** - 1 mL O\(_2\) = \( 1/22400 \) mol = **44.64 μmol** So, \[ 0.00081375\, \text{mL} \times 44.64\, \frac{\mu\text{mol}}{\text{mL}} = 0.03632\, \mu\text{mol/min/cm}^3 \] --- ### **Step 4: Convert from μmol/min/cm³ to μM/sec** - 1 cm³ = 1 mL = 1 × 10⁻³ L - μM = μmol/L So, per liter: \[ 0.03632\, \mu\text{mol} / \text{min} / 1 \text{ mL} = 36.32\, \mu\text{mol} / \text{min} / \text{L} \] But we want per second: \[ 36.32\, \mu\text{mol} / \text{min} / \text{L} \div 60 = 0.605\, \mu\text{mol} / \text{sec} / \text{L} \] So, the **metabolic O\(_2\) consumption rate** is: \[ \boxed{0.605\, \mu\text{M/sec}} \] --- ## **Final Answer** \[ \boxed{0.61\, \mu\text{M/sec}} \] (Rounded to two significant digits) --- ### **Summary of Steps** 1. **Calculate O\(_2\) content difference**: Δ[O2] = 0.2325 mL O2 / 100 mL blood 2. **Calculate O\(_2\) extracted**: \( Q \times \Delta[O_2] \) 3. **Convert to μmol/min**: \( 0.00081375\, \text{mL O}_2 \) × 44.64 μmol/mL 4. **Convert to μM/sec**: scale up to per liter, divide by 60. **Assumptions:** Only dissolved O\(_2\) considered. If you want to include hemoglobin-bound O\(_2\), you'll need Hb concentration and O\(_2\) saturation curves. For most tissues, bound O\(_2\) dominates. This answer is for dissolved O\(_2\) only. Let me know if you want the calculation including hemoglobin!