. What is the molecular weight of a pure gaseous compound having a density of 4.95 g/L at -35 oC and 1020 torr?
PM = dRT
P = 1020/760 = ?
M = molecular weight
d = 4.95 g/L
R = 0.08206
T = 273 + (-35)
Substitute and solve for M.
Well, figuring out the molecular weight might sound complicated, but fear not! Just think of it as finding the weight of a gas molecule who's got a lot on its plate (or its bonds, to be precise).
To calculate the molecular weight, we need to use a handy formula: molecular weight = (density x R x T) / P, where R is the ideal gas constant, T is the temperature in Kelvin, and P is the pressure.
Now, let's plug in the values:
- Given density = 4.95 g/L
- R = 0.0821 (we need to convert Torr to atmospheres)
- T = -35 + 273.15 (converting Celsius to Kelvin) = 238.15 K
- P = 1020 Torr / 760 Torr/atm (rounding off) = 1.342 atm
Using these values, we can calculate the molecular weight:
molecular weight = (4.95 x 0.0821 x 238.15) / 1.342
And voila! Using the magic of math (or a calculator), you'll find the molecular weight. Now, I won't spoil the fun by giving you the final answer directly. Why don't you grab your calculator and see what magical molecular weight you conjure up?
To find the molecular weight of a pure gaseous compound, we can 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, let's convert the temperature from degrees Celsius to Kelvin:
-35 oC + 273.15 = 238.15 K
Now we can rearrange the ideal gas law equation to solve for the number of moles:
n = (PV) / (RT)
Next, we'll convert the pressure from torr to atm:
1020 torr / 760 torr/atm = 1.342 atm
Now we have all the values necessary to calculate the number of moles:
n = (1.342 atm * 4.95 g/L) / (0.0821 L·atm/(mol·K) * 238.15 K)
n ≈ 0.114 mol
Finally, to find the molecular weight (also known as the molar mass) of the compound, we divide the mass by the number of moles:
Molecular weight = Mass / Moles
Since we're given the density (in g/L), we can calculate the mass as follows:
Mass = Density * Volume
Since we're looking for the molecular weight of the compound, we'll assume 1 liter as the volume:
Mass = 4.95 g/L * 1 L = 4.95 g
Now we can calculate the molecular weight:
Molecular weight = 4.95 g / 0.114 mol
Molecular weight ≈ 43.42 g/mol
Therefore, the molecular weight of the pure gaseous compound is approximately 43.42 g/mol.
To find the molecular weight of a pure gaseous compound, you will need to use the ideal gas law. The ideal gas law can be expressed as:
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 calculate the molecular weight, we will need to rearrange the ideal gas law equation as follows:
n = (PV) / (RT)
First, convert the given density from g/L to g/cm³ (since 1 L = 1000 cm³). The density is given as 4.95 g/L, so it becomes 4.95 g/cm³.
Next, convert the given temperature from degrees Celsius to Kelvin. The temperature is given as -35 oC, so it becomes -35 + 273.15 = 238.15 K.
Now, convert the given pressure from torr to atm. The pressure is given as 1020 torr, so it becomes 1020 torr / 760 torr/atm = 1.342 atm.
Now, substitute the values into the rearranged ideal gas law equation:
n = ((1.342 atm) * (V)) / ((0.0821 L·atm/(mol·K)) * (238.15 K))
Since we are trying to find the molecular weight, we can assume that the volume is 1 liter (V = 1 L). Substituting this value:
n = ((1.342 atm) * (1 L)) / ((0.0821 L·atm/(mol·K)) * (238.15 K))
Simplifying the equation:
n = 0.0728 mol
Finally, to calculate the molecular weight, we divide the given mass (4.95 g) by the number of moles (0.0728 mol):
Molecular weight = 4.95 g / 0.0728 mol
Therefore, the molecular weight of the pure gaseous compound is approximately 68.0 g/mol.