Helium-oxygen mixtures are used by divers to avoid the bends and are used in medicine to treat some respiratory ailments. What percent (by moles) of is present in a helium-oxygen mixture having a density of 0.498 at 25 and 721 ?

To determine the percentage of helium in a helium-oxygen mixture, we need to use the ideal gas law and the molar masses of helium and oxygen.

The ideal gas law is expressed as follows:
PV = nRT

Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature

First, we need to calculate the number of moles of helium and oxygen in the given mixture. We can use the ideal gas law rearranged to solve for the number of moles (n):

n = PV / RT

Given:
Density (ρ) = 0.498 g/L
Temperature (T) = 25 °C = 25 + 273.15 = 298.15 K
Pressure (P) = 721 mmHg

To convert the density to a molar mass, we'll use the Equation of State for Ideal Gases:

ρ = PM / RT

Where:
ρ = density
P = pressure
M = molar mass
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature

Rearranging the equation to solve for the molar mass (M):

M = ρRT / P

Calculating the molar masses of helium and oxygen:
Helium (He): M_He = ρRT_He / P_He
Oxygen (O2): M_O2 = ρRT_O2 / P_O2

Using the given values, we can calculate the molar masses of helium and oxygen in the mixture.

Once we have the molar masses, we can find the moles of helium (n_He) and moles of oxygen (n_O2) using the equation:

n = ρ / M

Finally, we can obtain the percentage of helium in the helium-oxygen mixture:

% of helium = (n_He / (n_He + n_O2)) * 100

By using the calculated molar masses and solving the expressions above, we can determine the percentage of helium in the mixture.