# An unknown gas is placed in a 1.500 L bulb at a pressure of 356 mm Hg and a temperature of 22.5 ∘C, and is found to weigh 0.8108g .What is the molecular mass of the gas?

## Why did the balloon go to the party alone? Because it didn't want to hear any bad "air" jokes! Now, let's figure out the molecular mass of this mysterious gas, shall we?

To solve this, we can use the Ideal Gas Law equation: PV = nRT.

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

First, let's convert the given pressure from mm Hg to atm, using the conversion factor: 1 atm = 760 mm Hg.

So, 356 mm Hg * (1 atm / 760 mm Hg) = 0.4684 atm.

We also need to convert the given temperature from Celsius to Kelvin, using the equation: K = °C + 273.15.

Therefore, 22.5 °C + 273.15 = 295.65 K.

Now, we can rearrange the Ideal Gas Law equation to solve for n (number of moles of gas): n = PV / RT.

Let's substitute the known values into the equation:
n = (0.4684 atm * 1.500 L) / (0.0821 L·atm/mol·K * 295.65 K).

After doing the math, we find that n ≈ 0.027 mol.

Now, let's find the molecular mass (molar mass) of the gas by dividing the mass of the gas (0.8108 g) by the number of moles (0.027 mol).

molecular mass = 0.8108 g / 0.027 mol.

After the calculation, the molecular mass of the gas is approximately 30 g/mol.

So, the molecular mass of the unknown gas is around 30 g/mol.

## To find the molecular mass of the gas, we can make use of 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)

Before we start, let's convert the given pressure, temperature, and volume to the appropriate units:

Pressure:
1 atm = 760 mm Hg
So, 356 mm Hg = 356/760 atm

Temperature:
In Kelvin, T = °C + 273.15
So, 22.5 °C = 22.5 + 273.15 K

Now we can substitute the values into the equation:

(356/760) atm * 1.500 L = n * 0.0821 L·atm/(mol·K) * (22.5 + 273.15) K

(356/760) * 1.500 = n * 0.0821 * 295.65

To find 'n', rearrange the equation:

n = ((356/760) * 1.500) / (0.0821 * 295.65)

Now, we can calculate 'n':

n ≈ 0.0188 mol

Now that we have the number of moles, we can calculate the molecular mass. The molecular mass (molar mass) is the mass of one mole of the substance.

molecular mass = mass / number of moles

molecular mass = 0.8108 g / 0.0188 mol

molecular mass ≈ 43.14 g/mol

Therefore, the molecular mass of the unknown gas is approximately 43.14 g/mol.

## To determine the molecular mass of the gas, we can use the ideal gas law equation:

PV = nRT

Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature

First, let's convert the given pressure from mm Hg to atm. We can use the conversion factor:

1 atm = 760 mm Hg

So, the pressure is 356 mm Hg * (1 atm / 760 mm Hg) = 0.4684 atm.

Next, let's convert the given temperature from degrees Celsius to Kelvin:

T(K) = T(°C) + 273.15
T(K) = 22.5 °C + 273.15 = 295.65 K

Now, let's rearrange the ideal gas law equation to solve for n (number of moles):

n = (PV) / (RT)

Substituting the given values:

n = (0.4684 atm * 1.500 L) / (0.0821 L·atm/mol·K * 295.65 K)
n = 2.278 mol

Now, we can determine the molecular mass of the gas by dividing the given mass (0.8108 g) by the number of moles (2.278 mol):

Molecular mass = Mass / Moles
Molecular mass = 0.8108 g / 2.278 mol
Molecular mass ≈ 0.356 g/mol

Therefore, the molecular mass of the gas is approximately 0.356 g/mol.

## Use PV = nRT and solve for n = number of mols. Then n = grams/molar mass. You know n and grams, solve for molar mass.

Don't forget P is in atm, V in L and T in kelvin