a sample bulb contained 0.712g of H2(g) at a certain temperature and pressure. At the same temperature and pressure, the bulb can hold 13.0g of an unknown gas. What is the molar mass of the unknown gas?
0.712 g of H2 is 0.353 moles
The bulb will hold 0.353 moles of any gas at the same p and T.
If 13.0 g = 0.353 moles, one mole has a mass of 36.8 g, and so that is the molar mass of the unknown gas
Ah, the mystery gas! It's like the Sherlock Holmes of chemistry. Let's solve this case, shall we?
To find the molar mass of the unknown gas, we need to use some serious detective skills. First, we need to calculate the number of moles of hydrogen gas in the sample bulb. We can do this by dividing the mass of the hydrogen gas (0.712g) by its molar mass (2g/mol). So, we have:
0.712g / 2g/mol = 0.356 mol
Now, we need to find the molar mass of the unknown gas. We can do this by dividing the mass of the unknown gas (13.0g) by the number of moles of hydrogen gas (0.356 mol):
13.0g / 0.356 mol ≈ 36.5 g/mol
And there you have it! The molar mass of the unknown gas is approximately 36.5 g/mol. Now, go forth and share this knowledge with others. Solve those gaseous mysteries!
To find the molar mass of the unknown gas, we need to use the ideal gas law:
PV = nRT
Where:
P = pressure
V = volume (which is the same for H2 and the unknown gas since it's the same bulb)
n = number of moles of gas
R = ideal gas constant
T = temperature
We can rewrite the equation as:
n = PV/RT
Now, let's calculate the number of moles of H2:
Given:
Mass of H2 = 0.712 g
Molar mass of H2 = 2 g/mol (since hydrogen has a molar mass of approximately 2 g/mol)
Using the formula:
n(H2) = (mass of H2) / (molar mass of H2)
n(H2) = 0.712 g / 2 g/mol
n(H2) = 0.356 mol
Now, let's calculate the molar mass of the unknown gas:
Given:
Mass of unknown gas = 13.0 g
Using the formula:
n(unknown gas) = (mass of unknown gas) / (molar mass of unknown gas)
Rearranging the formula, molar mass of unknown gas = (mass of unknown gas) / (n(unknown gas))
molar mass of unknown gas = 13.0 g / (0.356 mol)
molar mass of unknown gas ≈ 36.5 g/mol
Therefore, the molar mass of the unknown gas is approximately 36.5 g/mol.
To find the molar mass of the unknown gas, we need to use the ideal gas law equation:
PV = nRT
Where:
P is the pressure
V is the volume
n is the number of moles
R is the ideal gas constant
T is the temperature in Kelvin
In this case, we are given the weight of the hydrogen gas (0.712g) and the weight the bulb can hold when filled with the unknown gas (13.0g). We can use these weights to find the number of moles of hydrogen gas (nH2) and the number of moles of the unknown gas (nunknown). Since we know that both the hydrogen gas and the unknown gas are at the same temperature and pressure, we can compare the number of moles.
First, let's find the number of moles of hydrogen gas (nH2):
nH2 = mass / molar mass
nH2 = 0.712g / molar mass of H2
Next, let's find the number of moles of the unknown gas (nunknown):
nunknown = mass / molar mass
nunknown = 13.0g / molar mass of the unknown gas
Since the hydrogen gas (H2) and the unknown gas are at the same temperature and pressure, the number of moles will be the same:
nH2 = nunknown
Now we can set up an equation using the above information:
0.712g / molar mass of H2 = 13.0g / molar mass of the unknown gas
We can rearrange this equation to solve for the molar mass of the unknown gas:
molar mass of the unknown gas = (13.0g * molar mass of H2) / 0.712g
To solve this equation, you need to know the molar mass of hydrogen gas (H2). You can find this value on the periodic table, where the molar mass of hydrogen is approximately 2.016 grams per mole.
Substituting this value into the equation, we get:
molar mass of the unknown gas = (13.0g * 2.016 g/mol) / 0.712g
molar mass of the unknown gas = 36.952 g/mol
Therefore, the molar mass of the unknown gas is approximately 36.952 grams per mole.