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(g) is present in a helium-oxygen mixture having a density of 0.538g/L at 25celsius and 721mmHg ?
Responses
chemistry - bobpursley, Friday, September 26, 2008 at 8:26pm
change that density to stp.
what do u mean by change density to stp
Density of gases changes with temp and pressure. Didn't I set that up for you?
When the question refers to "change density to stp," it means that we need to convert the density of the gas mixture from its current conditions to standard temperature and pressure (STP). STP is defined as a temperature of 0 degrees Celsius (273.15 Kelvin) and a pressure of 1 atmosphere (760 mmHg or 101.325 kPa).
To convert the density to STP, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in L)
n = number of moles of gas
R = ideal gas constant (0.0821 L·atm/(K·mol))
T = temperature (in Kelvin)
First, let's convert the given conditions to STP:
Given:
Density = 0.538 g/L
Temperature = 25 degrees Celsius = 25 + 273.15 = 298.15 Kelvin
Pressure = 721 mmHg
Convert the pressure to atm:
Pressure = 721 mmHg / 760 mmHg/atm = 0.9474 atm
Now we can calculate the volume:
Density = mass/volume
Volume = mass/density
Volume = 1 g / 0.538 g/L = 1.86 L
Now let's substitute the known values into the ideal gas law equation to find the moles of gas:
PV = nRT
n = (PV) / (RT)
n = (0.9474 atm) * (1.86 L) / (0.0821 L·atm/(K·mol) * 298.15 K)
n ≈ 0.097 mol
Now we need to find the number of moles of helium (He) in the gas mixture. Let's assume the mixture has 100% helium. Therefore, the moles of helium in the mixture is equal to the total moles of gas.
Moles of He = Moles of gas = 0.097 mol
Finally, we can calculate the percent (by moles) of helium in the mixture:
Percent of He = (Moles of He / Total moles of gas) * 100
Percent of He = (0.097 mol / 0.097 mol) * 100
Percent of He = 100
Therefore, the percent (by moles) of helium in this helium-oxygen mixture is 100%.
When the question asks you to "change the density to STP," it is referring to the Standard Temperature and Pressure (STP) conditions. The STP conditions are defined as a temperature of 0 degrees Celsius (273.15 Kelvin) and a pressure of 1 atmosphere.
To change the density from the given conditions (25 degrees Celsius and 721 mmHg) to STP, we need to apply the ideal gas law. The ideal gas law equation is:
PV = nRT
where:
P = pressure
V = volume
n = moles of gas
R = ideal gas constant
T = temperature in Kelvin
First, convert the given temperature of 25 degrees Celsius to Kelvin:
T(in Kelvin) = T(in Celsius) + 273.15
T = 25 + 273.15 = 298.15 K
Next, convert the given pressure of 721 mmHg to atmospheres:
1 atmosphere = 760 mmHg
P(in atmospheres) = P(in mmHg) / 760
P = 721 mmHg / 760 = 0.9487 atmospheres
Now, we have the temperature (T = 298.15 K) and pressure (P = 0.9487 atm) at the current conditions. We can calculate the moles of gas using the ideal gas law equation.
Rearranging the ideal gas law equation, we get:
n = PV / RT
Substituting the values, we have:
n = (0.538 g/L) / (0.0821 L*atm/mol*K * 298.15 K)
n = 0.0211 moles
Now that we have determined the moles of gas, we can calculate the percent of He (by moles) present in the mixture.
Let's assume that the mixture is made up of He and O2 gases only. The molecular weights of He and O2 are 4 g/mol and 32 g/mol, respectively.
To find the percent of He gas (by moles) in the mixture, we divide the moles of He by the total moles of gas in the mixture and multiply by 100.
Percent of He = (moles of He / total moles of gas) * 100
Percent of He = (0.0211 moles He / 0.0211 moles) * 100
Percent of He = 100%
Therefore, the mixture consists of 100% He gas by moles.