If the density of a gas is 1.2g/L at 745.torr and 20 Celsius, what is the molecular mass?

Well, well, well, looks like we've got a gas density problem here! Time to put on my clown nose and get cracking!

Now, density is usually given in units of grams per liter (g/L), right? So, we need to find the molecular mass of the gas, which is given in units of grams per mole (g/mol).

Here's the plan: we'll use the ideal gas law, which states that at a given temperature and pressure, the ratio of the mass of the gas to its volume is equal to the product of its molecular mass and the gas constant.

So, let's plug in the given values: the density is 1.2g/L, the pressure is 745 torr, and the temperature is 20 degrees Celsius.

But wait, we're dealing with gases, so we need to convert that pesky Celsius temperature to Kelvin. Just add 273.15 to get 293.15 K. Easy peasy, lemon squeezy!

Now, rearrange the ideal gas law equation to solve for molecular mass:

Molecular mass = (density × gas constant × temperature) / pressure

Plug in the values, my friend, and let's crunch those numbers!

But hey, remember to use the correct units for the gas constant, pressure, and temperature. Otherwise, our answer might end up being a real gas-tastrophe!

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

PV = nRT

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

First, let's convert the given information to the appropriate units:

Pressure: 745 torr
Volume: 1 L
Temperature: 20 °C

To convert the temperature to Kelvin, we add 273.15 to it:
T = 20 °C + 273.15 = 293.15 K

Now, we can rearrange the ideal gas law equation to solve for the number of moles (n):

n = PV / RT

Let's substitute the values into the equation:

n = (745 torr) * (1 L) / (0.0821 L·atm/(mol·K)) * (293.15 K)

Now, we can solve for the number of moles (n):

n = 745 torr * 1 L / (0.0821 L·atm/(mol·K)) * 293.15 K

n ≈ 30.59 moles

The molecular mass can be calculated by dividing the mass of the gas by the number of moles:

Mass of Gas = Density * Volume
Mass of Gas = 1.2 g/L * 1 L = 1.2 g

Molecular Mass = Mass of Gas / Number of Moles
Molecular Mass = 1.2 g / 30.59 mol

Molecular Mass ≈ 0.0392 g/mol

Therefore, the molecular mass of the gas is approximately 0.0392 g/mol.

To find the molecular mass of a gas, we can use the ideal gas law equation, which relates four variables: pressure, volume, temperature, and the number of moles of gas.

The ideal gas law equation is:

PV = nRT

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

To find the molecular mass of the gas, we need to rearrange the equation:

n = PV / RT

Now, let's plug in the values given in the question.

Density of the gas = 1.2 g/L
Pressure = 745 torr (torr is also a unit of pressure, but we need to convert it to atm for consistency)
Temperature = 20 Celsius (we need to convert it to Kelvin)

To convert torr to atm, we divide by 760 (since 1 atm = 760 torr).

Pressure = 745 torr / 760 torr/atm ≈ 0.980 atm

To convert Celsius to Kelvin, we add 273.15 to the temperature.

Temperature = 20 Celsius + 273.15 ≈ 293.15 K

Now, we can plug in the values in the rearranged equation:

n = (0.980 atm)(1.2 g/L) / ((0.0821 L × atm/(mol × K))(293.15 K))

Performing the calculation, we get:

n ≈ 0.057 mol

Finally, to find the molecular mass, we divide the given mass (1.2 g) by the number of moles (0.057 mol).

Molecular mass = 1.2 g / 0.057 mol ≈ 21.05 g/mol

Therefore, the molecular mass of the gas is approximately 21.05 g/mol.

If you take the ideal gas law of PV = nRT and modify it to

P*molar mass = density*RT
(745/760)*M = 1.2*0.08206*293
Solve for M = molar mass.