Question

1. Arterial blood contains about 0.25 mg of oxygen per milliliter. What is
the pressure exerted by the oxygen in one liter of arterial blood at normal
body temperature of 37.4C? ​

Answer 1

Answer:

Explanation:

Hi there,

Sorry for the late reply. To get started, please recall the osmotic pressure formula:

$\pi = cRTi$    where π is the osmotic pressure in standard atmosphere (atm), R is the gas constant 0.082057 L*atm*mol-1*K-1, T is temperature in Kelvin (K), and i is the Van't Hoff Factor.

In this problem, we are given the density of diatomic oxygen O₂ but can convert it to concentration, c, using molar mass or molecular weight of diatomic oxygen. Similarly, we are given the temperature, but must be converted to Kelvin (K). R and i are constants, and the Van't Hoff factor of diatomic oxygen is 1. This is because oxygen does not split into simpler single O atoms when in solution, hence stays as 1 molecule.

First, let's convert our variables into the desired, start with concentration:

$c_M = \frac{n}{V_L} =\frac{\rho}{MM_O_2 } = \frac{m_g}{V_L(MM_O_2)}$  Rho (Greek p-like letter) is density in g/L.The subscripts indicate unit; concentration needs unit of Molars (M), Volume must be in liters (L), and mass in grams (g). MM is molar mass of diatomic oxygen.

$c_M = \frac{n}{V_L} = \frac{m_g}{V_L(MM_O_2)}= \frac{0.25 g \ O_2}{(1 L)(31.998g \ O_2/mol \ O_2)}= 0.00781 \ mol \ O_2 / L$ notice we did not have to convert the mg/mL to g/L... SI prefix/SI prefix will result in same number if you moved both numbers to another SI prefix.  

Now, let's convert temperature:

$T_K=(37.4C+273.15 C)\frac{K}{C} =310.55 K$

Now, we can solve for osmotic pressure:

$\pi =cRTi=(0.00781 \ mol \ O_2/L)(0.082057 L*atm*mol^{-1} *K^{-1} )(310.55K)(1) \\ \pi =0.199 \ atm$

If you prefer to round for sig figs, you can keep it as 0.20 atm.

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thanks,

Answer 2

Osmotic pressure prevents the backflow of liquids and is important in the circulatory system. At normal temperature, the oxygen exerts a pressure of 0.199 atm.

What is osmotic pressure?

Osmotic pressure (π) is the force applied to the solution to avoid the backflow of the solvent through the membrane. It prevents the inward flow of blood in the body.

Given,

Density of oxygen in blood = 0.25 mg/mL

Volume (V) = 1 L

Temperature (T) = 37.4 °C = 310.55 K

Gas constant (R) = 0.082057

The formula for osmotic pressure is given as,

π = icRT

Here, i is van't Hoff factor and c is molar concentration.

The molarity (concentration) is calculated as,

Molarity = moles ÷ volume

= mass ÷ (molar mass × volume)

= 0.25 gm ÷ (32 gm/mol × 1 L)

= 0.00781 mol /L

Substituting values in osmotic pressure as:

π= icRT

= 1 × 0.00781 mol /L × 0.082057 × 310.55 K

= 0.199 atm

Therefore, the blood applies pressure of 0.199 atm in one liter of blood.

Learn more about osmotic pressure here:

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