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 helium is present in a helium-oxygen mixture having a density of 0.538 g/L at 25 degrees C and 721mmHg?
Express your answer numerically as a percentage.
To determine the percent by moles of helium in the mixture, we need to use the ideal gas law equation:
PV = nRT
Where:
P = pressure (721 mmHg)
V = volume (unknown)
n = number of moles of gas (unknown)
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (25°C + 273.15 = 298.15 K)
First, let's determine the number of moles of helium:
PV = nRT
n = PV / RT
n = (721 mmHg) * V / (0.0821 L·atm/mol·K * 298.15 K)
n = 0.0067641 V
Next, we'll determine the density of the mixture using the given values:
density = mass / volume
0.538 g/L = mass / V
Now, we can express the mass of the mixture using moles and molar mass:
mass = n * molar mass
0.538 g/L = 0.0067641 V * (4 g/mol) (since the molar mass of helium is 4 g/mol)
Simplifying the equation:
0.538 g/L = 0.0270564 V
Now, we can solve for V using the density:
V = 0.538 g/L / 0.0270564
V = 19.884 L
Finally, we can calculate the percent by moles of helium:
n = 0.0067641 * 19.884
n = 0.13455457404 mol
The percent of helium by moles in the mixture is:
(0.13455457404 mol / 0.13455457404 mol) * 100%
= 100%
Therefore, the percent (by moles) of helium in the helium-oxygen mixture is 100%.
To determine the percent of helium (by moles) in the helium-oxygen mixture, we need to use the ideal gas law equation:
PV = nRT
Where:
P = Pressure in atmospheres (converted from mmHg)
V = Volume in liters
n = Number of moles
R = Ideal gas constant (0.0821 L·atm/(mol·K))
T = Temperature in Kelvin (converted from degrees Celsius)
First, let's convert the density of the mixture from g/L to g/cm³ (cubic centimeter) since the ideal gas law uses the volume in liters and the density in grams per cubic centimeter can be directly converted to grams per liter:
0.538 g/L * (1 cm³ / 1 mL) * (1 L / 1000 mL) = 0.000538 g/cm³
Next, let's determine the number of moles of the mixture by using the equation:
moles = mass / molar mass
Since the density is given, we can determine the mass of the mixture in grams by multiplying the density by the volume of the mixture in cm³. Then, we divide this mass by the molar mass of the mixture to get the number of moles.
Now we need to find the molar mass of the helium-oxygen mixture. Since we are given the percentage of helium, we assume that the remaining percentage is oxygen. The molar mass of helium is 4.0026 g/mol, and the molar mass of oxygen is 16.00 g/mol.
Let's assume we have 100 grams of the mixture, which means if X% is helium, then (100 - X)% is oxygen.
Calculating the moles of helium:
mass of helium = 0.01X * 100g
moles of helium = (0.01X * 100g) / molar mass of helium = (0.01X * 100g) / 4.0026 g/mol
Calculating the moles of oxygen:
mass of oxygen = (1 - 0.01X) * 100g
moles of oxygen = [(1 - 0.01X) * 100g] / molar mass of oxygen = [(1 - 0.01X) * 100g] / 16 g/mol
Using the ideal gas law, we can now determine the moles of the mixture:
PV = nRT
n = (PV) / (RT)
n = [(0.000538 g/cm³) * (V cm³)] / [(0.0821 L·atm/(mol·K)) * (T K)]
Since the volume is given in liters and the density is given in grams per cubic centimeter, we need to convert the volume to cm³:
1 L = 1000 cm³
Now we can substitute the values into the equation and solve for the number of moles:
n = [(0.000538 g/cm³) * (V * 1000 cm³)] / [(0.0821 L·atm/(mol·K)) * (T K)]
To convert the number of moles of helium to a percentage, divide the moles of helium by the total moles of the mixture (moles of helium + moles of oxygen) and multiply by 100 to get the percentage.
percent helium = (moles of helium / (moles of helium + moles of oxygen)) * 100
Note: The percent helium calculation assumes that the masses and volumes are for a total system of 100 grams and 100 liters, respectively. If the given mass or volume is different, you should adjust the calculations accordingly.
Plug in the values given in the question (density, temperature, and pressure) and the calculated values above into the equations to find the percent (by moles) of helium in the helium-oxygen mixture.