I don't understand how to answer this questions. I thought molecular weight was adding up the atomic weight of each element in a molecule...?
If a 0.614g sample of a gas maintains a pressure of 238 mmHg when contained in a 1.0L flask at 0.0 degree Celcius, what is the gas's molecular weight?
You're right but there are other ways to obtain the molecular weight than adding up the atomic weights of each element.
In this case, PV = nRT is the universal gas equation.
You know P (change to atmospheres), You know V (in liters), you know R and you know T(must be in Kelvin and note the correct spelling of celsius). The only unknown in this equation is n, the number of moles of the gas.
Then mols gas = grams/molecular weight. You know mols from the calculation, you know grams from the problem, calculate molecular weight.
To determine the gas's molecular weight, you need to use the ideal gas law equation and its rearrangement.
The ideal gas law equation is:
PV = nRT,
where:
P is the pressure of the gas,
V is the volume of the gas,
n is the number of moles of gas,
R is the ideal gas constant (0.0821 L·atm/(mol·K)), and
T is the temperature in Kelvin.
To rearrange the equation to solve for n (number of moles), you divide both sides of the equation by RT:
n = PV / RT.
To calculate the number of moles, you need to convert the given pressure in mmHg to atm and the temperature in degrees Celsius to Kelvin.
1 atm = 760 mmHg (approximately)
To convert temperature from Celsius to Kelvin, add 273.15 to the Celsius temperature.
Now, substituting the given values into the equation:
P = 238 mmHg / 760 mmHg/atm = 0.3132 atm
V = 1.0 L
T = (0.0°C + 273.15) K = 273.15 K
R = 0.0821 L·atm/(mol·K)
Plugging these values into the equation:
n = (0.3132 atm) * (1.0 L) / (0.0821 L·atm/(mol·K) * 273.15 K)
Calculating the number of moles:
n = 0.0131 mol
Now that you know the number of moles (n), you can calculate the molecular weight (MW) using the formula:
MW = mass / moles.
The given mass of the gas is 0.614 g.
So, MW = 0.614 g / 0.0131 mol.
Simplifying this calculation:
MW ≈ 46.86 g/mol.
Therefore, the molecular weight of the gas is approximately 46.86 g/mol.