Question

The circulation of blood in the human body supplies ${O_2}$ and releases $C{O_2}$. The concentration of ${O_2}$ and $C{O_2}$ is variable but on the average, 100 ml blood contains 0.02g of ${O_2}$ and 0.08g $C{O_2}$. The volume of ${O_2}$ and $C{O_2}$ at 1 atm and body temperature, assuming 10 litre blood in human body is:
A. 2 litre, 4 litre
B. 1.5 litre, 4.5 litre
C. 1.59 litre, 4.62 litre
D. 3.82 litre, 4.62 litre

Answer 1

Hint: The general gas law is PV=nRT. It follows that no matter how we change the state of the given amount of gas the ratio PV/T always remains constant.

Complete step by step solution:
R is a Rydberg constant which is independent of all variables and popularly known as universal constant .Values of R :
R=0.0821 litre atm /k mol=8.314 J/k mol
 The general gas law has been derived out of so many laws such as
Boyle's law states” at constant temperature, the volume of a fixed mass of gas is inversely proportional to its pressure”.
Charles law which states that” at constant pressure, the volume of a fixed mass of a gas is proportional to its temperature” .
Gay lussacs law which states that “at constant volume, the pressure of a fixed mass of gas is proportional to the temperature”.
Avogadro’s law states that” the amount of gas in moles is proportional to the volume of the gas”.
In the question we are given with that , 100 ml blood contains 0.02g of ${O_2}$ and 0.08g $C{O_2}$ where the volume of ${O_2}$ and $C{O_2}$ at 1 atm and body temperature is to be calculated,
Using ideal gas equation
PV=nRT
Substituting the values from the question we get,
$
  1 \times {V_{{O_2}}} = \dfrac{2}{{32}} \times 0.0821 \times 310 = 1.59L \\
  1 \times {V_{C{O_2}}} = \dfrac{8}{{44}} \times 0.0821 \times 310 = 4.62L \\
$
Hence the correct option is C.

Note:
We are given an assumption of 10 L blood in the human body in a bigger scenario which makes 10000 ml if 1L has 1000 ml.