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 He is present in a helium-oxygen mixture having a density of 0.528g/L at 25 degree celsius and 721 mmHg ?

To determine the percent by moles of helium (He) in a helium-oxygen mixture, we need to use the ideal gas law equation: PV = nRT, where P represents the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.

Given:
Density (d) = 0.528 g/L
Temperature (T) = 25°C = 25 + 273.15 = 298.15 K
Pressure (P) = 721 mmHg

First, we need to convert the density to the molar mass using the ideal gas equation PV = mRT, where m represents mass.

Using the equation, we can rearrange it to solve for molar mass (M):
M = (mRT) / (PV)

The molar mass of a mixture containing helium (He) and oxygen (O2) is given by:
M = (n1 * M1 + n2 * M2) / (n1 + n2), where n1 and n2 represent the number of moles of helium and oxygen, and M1 and M2 represent the molar masses of helium (4 g/mol) and oxygen (32 g/mol).

Since the density (d) is given in grams per liter (g/L), we can convert it to grams per cubic centimeter (g/cm³) by dividing by 1000.

Density (d) = m / V
0.528 g/L = m / V

Since the volume (V) is not given, we can assume it to be 1 L, therefore:
0.528 g/L = m / 1 L
m = 0.528 g

Now, we can substitute the given values into the equation for molar mass:
M = (mRT) / (PV)
M = (0.528 g * 0.0821 L·atm/(mol·K) * 298.15 K) / (721 mmHg * 1 atm/760 mmHg)

Simplifying the equation:
M = (0.528 g * 0.0821 * 298.15 K) / (721 * 760)

Now, we can calculate the molar mass (M) of the mixture.

Next, we can calculate the number of moles (n1) of helium using the molar mass (M) and the molar mass of helium (4 g/mol):
n1 = (M1 * M) / (M1 + M2)
n1 = (4 g/mol * M) / (4 g/mol + 32 g/mol)

Finally, we can calculate the percent by moles of helium (He) in the mixture:
Percent by moles of helium = (n1 / (n1 + n2)) * 100

By following these steps, you can calculate the percent by moles of helium in the helium-oxygen mixture.