Myoglobin (Mb) is a protein containing a hem (iron) group. Myoglobin is an enzyme that allows storag — Analytical Chemistry Chemistry Question
Myoglobin for oxygen storage
Myoglobin (Mb) is a protein containing a hem (iron) group. Myoglobin is an enzyme that allows storage of oxygen. Each myoglobin molecule can reversibly bind one oxygen molecule according to the equation:
Mb + O2 ⇌ MbO2
This oxygen storage is important for diving animals such as whales. We are going to investigate how whales use it.
The fraction of Mb that is bound to oxygen increases with the oxygen concentration as:
Y = cO2 / (cO2 + Kc) , wherein Kc is a constant.
Oxygen is only slightly soluble in water: the amount that dissolves is proportional to the oxygen pressure: cO2 ∝ pO2
The fraction of Mb bound is then related to the oxygen pressure by:
Y = pO2 / (pO2 + Kp) wherein Kp is a constant.
The graph below is showing this relation (the scale of the graph is logarithmic!)
Determine the value and the unit of the constant Kp in the formula above (use the graph).
Model Answer
Take at the X-axis 100, this corresponds with 0.5 at the Y-axis, thus
0.5 = 100 / (100 + Kp)
50 + 0.5 Kp = 100
Kp = 100
The Mb molecule has the dimensions of 4.5 × 3.5 × 2.5 nm meaning that Mb fits in a box with these dimensions. Because the molecule is roughly elliptical in shape it will have a volume of about one half of the volume of the box. Proteins have a density of about 1400 kg m–3. The Avogadro number is NA = 6.02×10^23 mol-1.
Estimate the molar mass of Mb.
Model Answer
Volume of myoglobin VMb:
VMb = 0.5 × 4.5 nm × 3.5 nm × 2.5 nm = 19.7 nm^3 = 19.7×10–27 m^3
Molecular mass of Mb, MMb:
MMb = VMb × ρMb × NA = 19.7×10–27 m^3 × 1400 kg m–3 × 6.02×10^23 mol–1 = 16.6 kg mol–1
Whales obtain their oxygen by breathing air. They can stay under water for a long time using their oxygen storage. Assume that 20 % of the mass of their muscular tissues consists of myoglobin.
Calculate how many moles of oxygen the whale can store per kilogram of tissue.
Model Answer
1 kg Mb is 1/16.6 mol: 20 % is 0.2/16.6 = 0.012 mol kg–1
Oxygen is used to produce energy (heat and motion) by burning fat. The overall equation can be approximated by:
(CH2)n + 1.5 n O2 → n CO2 + n H2O
The energy released by this type of reaction is about 400 kJ per mole of oxygen. A large animal, such as a whale, needs to dissipate about 0.5 W per kg of mass of muscle tissue to stay warm and keep moving.
Calculate how long the whale can stay under water.
Model Answer
400 kJ mol–1 → 400 000 × 0.012 J kg–1 of muscle tissue
W = J s–1 ⇒ per second per kg of muscle tissue 0.5 J.
Time = (400000 × 0.012) / 0.5 = 9600 s = 2 hours and 40 minutes
Give the equation for the burning of a real fat molecule:
Model Answer
(CH2)3n+6 (CO2)3H2 + (4.5n + 9.5) O2 → (3n + 9)O2 + (3n + 7) H2O