a gas sample is collected at 16 degrees c and 0.982 atm. if the sample has a mass of 7.40 g and a volume of 3.96 l, find the volume of the gas at stp and the molar mass?
Use PV = nRT and the first set of conditions and solve for n = number of mols.
n = grams/molar mass. You know n and grams, solve for molar mass.
Since 1 mol of a gas occupies 22.4L at STP, then volume @ STP is n x 22.4 = ?
Well, let's see. To calculate the volume of the gas at STP (Standard Temperature and Pressure), we need to use the combined gas law equation: PV = nRT. But don't worry, I won't let this equation put any pressure on you!
First, let's convert the temperature to Kelvin because gases like to keep it cool. To do that, we add 273 to our Celsius temperature. So, 16 degrees Celsius is equal to 289 Kelvin.
Next, let's calculate the number of moles (n) of the gas using the ideal gas law equation: PV = nRT. However, we need to manipulate the equation to solve for n.
Dividing both sides of the equation by RT, we get n = PV / RT. Don't worry, this calculation is not as complicated as it sounds!
Using the values given, we have:
n = (0.982 atm) * (3.96 L) / [(0.0821 L*atm/(mol*K)) * (289 K)]
Simplifying the equation, we find that n ≈ 0.171 moles.
Now, to find the molar mass of the gas, we divide the mass of the gas by the number of moles. So the molar mass is approximately 7.40 g / 0.171 moles.
Drumroll, please...
Approximately, the molar mass is 43.27 g/mol.
As for the volume at STP, that would be equal to 22.4 liters per mole. So, our final answer is 22.4 L. Ta-da!
I hope I didn't gas you out with all these calculations. Remember, laughter is the best gas-reliever!
To find the volume of the gas at standard temperature and pressure (STP), we need to use the ideal gas law equation:
PV = nRT
Where:
P = pressure of the gas sample
V = volume of the gas sample
n = number of moles of gas
R = ideal gas constant
T = temperature of the gas sample
First, let's calculate the number of moles using the ideal gas law equation. Rearranging the equation, we have:
n = PV / RT
Substituting the values, we get:
n = (0.982 atm * 3.96 L) / (0.0821 atm L / mol K * 16 + 273)
n = 0.0404 mol
Now, to find the volume of the gas at STP, we can use the molar volume of an ideal gas at STP, which is approximately 22.4 L/mol.
Volume at STP = n * 22.4 L/mol
Volume at STP = 0.0404 mol * 22.4 L/mol
Volume at STP = 0.9056 L
Therefore, the volume of the gas at STP is approximately 0.9056 L.
To find the molar mass of the gas, we can use the formula:
molar mass = mass of sample (g) / number of moles
Substituting the values, we get:
molar mass = 7.40 g / 0.0404 mol
molar mass = 182.67 g/mol
Therefore, the molar mass of the gas is approximately 182.67 g/mol.
To find the volume of the gas at STP (Standard Temperature and Pressure) and the molar mass, we can use the Ideal Gas Law equation, which is:
PV = nRT
Where:
P = Pressure of the gas
V = Volume of the gas
n = Number of moles of the gas
R = Ideal Gas Constant
T = Temperature of the gas in Kelvin
First, let's convert the given temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 16 + 273.15 = 289.15 K
Now we can substitute the given values into the Ideal Gas Law equation:
PV = nRT
P = 0.982 atm
V = 3.96 L
n = ? (to be determined)
R = 0.0821 L • atm/mol • K (Ideal Gas Constant)
T = 289.15 K (temperature in Kelvin)
Let's rearrange the equation to solve for n (number of moles):
n = PV / RT
n = (0.982 atm) * (3.96 L) / (0.0821 L • atm/mol • K * 289.15 K)
Calculating the equation gives us:
n ≈ 0.165 moles
Now that we have the number of moles, we can find the molar mass using the formula:
Molar Mass (g/mol) = mass (g) / moles
Molar Mass (g/mol) = 7.40 g / 0.165 moles ≈ 44.85 g/mol
So, the volume of the gas at STP is unknown until the molar mass is determined. The molar mass is approximately 44.85 g/mol.