A sample of a breathing mixture for divers contained 34.3% helium, He; 51.7% nitrogen, N2; and 14.0% oxygen, O2 (by mass). What is the density of this mixture at 22°C and 748 mmHg?
I keep getting d=0.00441. I'm not sure what I'm doing wrong. My equation with the numbers substituted in looks like this: (0.98421)(0.10853)=d(0.08206)(295.15)
He gave you the wrong formula.
I know that this is over a year after you posted, but you should actually just use the formula d=PM(molar mass)/RT.
To find the density of the breathing mixture, we need to use the ideal gas law. The ideal gas law is given by:
PV = nRT
Where:
P = pressure in atmospheres
V = volume in liters
n = number of moles
R = gas constant (0.0821 L.atm/mol.K)
T = temperature in Kelvin
Given:
Pressure (P) = 748 mmHg
Temperature (T) = 22°C = 295.15 K
To calculate the density, we need to convert the given percentage composition into moles.
Let's assume we have 100 g of the breathing mixture.
Mass of helium (He) = 34.3% of 100g = 34.3g
Mass of nitrogen (N2) = 51.7% of 100g = 51.7g
Mass of oxygen (O2) = 14.0% of 100g = 14g
Next, we need to convert these masses into moles by dividing them by their respective molar masses.
Molar mass of helium (He) = 4.00 g/mol (approx.)
Number of moles of helium (He) = 34.3g / 4.00 g/mol = 8.575 mol
Molar mass of nitrogen (N2) = 28.02 g/mol
Number of moles of nitrogen (N2) = 51.7g / 28.02 g/mol = 1.846 mol
Molar mass of oxygen (O2) = 32.00 g/mol
Number of moles of oxygen (O2) = 14g / 32.00 g/mol = 0.438 mol
Now we can calculate the total number of moles in the mixture:
Total moles = moles of helium + moles of nitrogen + moles of oxygen
= 8.575 mol + 1.846 mol + 0.438 mol
= 10.859 mol
Now we can substitute these values into the ideal gas law equation.
PV = nRT
(748 mmHg) (V) = (10.859 mol) (0.0821 L.atm/mol.K) (295.15 K)
Now we can solve for V, which is the volume in liters:
V = (10.859 mol) (0.0821 L.atm/mol.K) (295.15 K) / (748 mmHg)
Note: We need to convert mmHg to atm by dividing by 760 mmHg/atm:
V = (10.859 mol) (0.0821 L.atm/mol.K) (295.15 K) / (748 mmHg / 760 mmHg/atm)
V = 23.686 L
Finally, we can calculate the density using the formula:
Density (ρ) = mass / volume
Since we assumed we have 100g of the breathing mixture, the density is:
Density = 100g / 23.686 L
≈ 4.2 g/L
Therefore, the density of the breathing mixture is approximately 4.2 g/L at 22°C and 748 mmHg.
I would use a modified form of PV = nRT that is P*molar mass = dRT for density.
You need to calculate the molar mass of the mixture of gases which cn be done by
0.343 x molar mass He = ??
0.517 x molar mass N2 = ??
0.140 x molar mass O2 = ??
Add. The sum is the molar mass of the mixture. Then substitute the conditions of T and P and solve for density.