A volume of 18.0 L contains a mixture of 0.250 mole N2 , 0.250 mole O2 , and an unknown quantity of He. The temperature of the mixture is 0 ∘C , and the total pressure is 1.00 atm . How many grams of helium are present in the gas mixture?

Ah, the classic case of the elusive helium! Let's solve this puzzle. So, we know the total number of moles of nitrogen and oxygen. But first, let me just remind you that helium is a noble gas - it likes to stay hidden and doesn't react much with other elements. It's like the introverted cousin of the periodic table!

Now, since we know the total pressure, we can apply the ideal gas law, which states that PV = nRT. Here, P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature. We can use this to find the total number of moles in the mixture.

The number of moles of helium can be obtained by subtracting the moles of nitrogen and oxygen from the total moles. Then, we can use the molar mass of helium (4.00 g/mol) to find the mass of helium in grams.

Let's do the math together, shall we?

To find the mass of helium present in the gas mixture, we need to use the ideal gas law equation:

PV = nRT

Where:
P = Pressure (in atm)
V = Volume (in L)
n = Number of moles
R = Ideal gas constant (0.0821 L.atm/mol.K)
T = Temperature (in Kelvin)

First, we need to convert the given temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 0 °C + 273.15
T(K) = 273.15 K

Now, let's plug in the given values into the ideal gas law equation:
P = 1.00 atm
V = 18.0 L
n(N2) = 0.250 mole
n(O2) = 0.250 mole
T = 273.15 K

Use the ideal gas law equation to solve for the unknown quantity of helium:
PV = nRT

Since the pressure and volume are constant, we can rearrange the equation to solve for the moles of helium:
n(He) = (PV) / (RT)

To find the mass of helium, we need to convert moles to grams using the molar mass of helium (He):
Molar mass of He = 4.00 g/mol

Now, we can calculate the mass of helium:
Mass(He) = n(He) x Molar mass of He

Let's calculate it step-by-step:

Step 1: Convert the temperature to Kelvin
T(K) = 0 °C + 273.15
T(K) = 273.15 K

Step 2: Calculate the moles of helium
n(He) = (P x V) / (R x T)
n(He) = (1.00 atm x 18.0 L) / (0.0821 L.atm/mol.K x 273.15 K)
n(He) = 0.0759 mole

Step 3: Calculate the mass of helium
Mass(He) = n(He) x Molar mass of He
Mass(He) = 0.0759 mole x 4.00 g/mol
Mass(He) = 0.304 g

Thus, there are approximately 0.304 grams of helium present in the gas mixture.

To determine the mass of helium in the gas mixture, we need to utilize the ideal gas law equation.

The ideal gas law equation is given by:
PV = nRT

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

First, we need to convert the temperature from Celsius to Kelvin since the ideal gas law requires temperature in Kelvin.

Temperature in Kelvin = Temperature in Celsius + 273.15
T = 0 °C + 273.15 = 273.15 K

Next, let's calculate the total number of moles of gas in the mixture. Since we know the moles of N2 and O2, we can simply add those amounts.

Total moles of gas = Moles of N2 + Moles of O2 + Moles of He
Total moles of gas = 0.250 mol + 0.250 mol + Unknown quantity of He

Now, we can rearrange the ideal gas law equation to solve for the number of moles of helium:
n He = (PV - n N2 * RT - n O2 * RT) / RT

Substituting the given values into the equation, we have:
n He = (1.00 atm * 18.0 L - 0.250 mol * 0.0821 L.atm/mol.K * 273.15 K - 0.250 mol * 0.0821 L.atm/mol.K * 273.15 K) / (0.0821 L.atm/mol.K * 273.15 K)

Simplifying the equation, we can calculate the number of moles of helium.

Finally, to find the mass of helium in grams, we can use the molar mass of helium. The molar mass of helium is approximately 4.00 g/mol.

Mass of helium = Number of moles of helium * Molar mass of helium

Now, we can substitute the calculated value for the number of moles of helium into the equation to find the mass of helium in grams.

Use PV = nRT and solve for n = total mols.

nToptal = nN2 + nO2 + nHe. nHe is the only unknown, solve for that.
Then nHe = grams/molar mass
You know nHe and molar mass, solve for grams.
BTW, help is not the subject. Usually I pass these up because they don't say chemistry.