At 22 degrees Celsius and a pressure of 755 mm Hg, an unknown gas was found to have a density of 4.52 g/L. When analyzed, the gas was found to consist of two elements: Boron at 78.1% and Hydrogen at 21.9%.
What is the molecular formula of this unknown gas?
To determine the molecular formula of the unknown gas, we need to calculate the molar mass of the gas using the given percentages of Boron and Hydrogen.
1. Calculate the molar masses of Boron (B) and Hydrogen (H):
- The molar mass of Boron (B) is approximately 10.81 g/mol.
- The molar mass of Hydrogen (H) is approximately 1.01 g/mol.
2. Calculate the average molar mass of the unknown gas:
- Multiply the molar mass of Boron by its percentage (0.781):
Average molar mass = (10.81 g/mol) * (0.781)
- Multiply the molar mass of Hydrogen by its percentage (0.219):
Average molar mass += (1.01 g/mol) * (0.219)
- Sum these calculations:
Average molar mass = (10.81 g/mol * 0.781) + (1.01 g/mol * 0.219)
3. Now let's calculate the volume occupied by one mole of the gas using the density:
- Given density = 4.52 g/L
- Calculate the volume that corresponds to one mole of the gas using the molar mass calculated in step 2:
Volume of 1 mole = (1 mol) / (4.52 g/L / average molar mass)
4. Calculate the number of moles of each element in one mole of the gas:
- Multiply the molar mass of Boron by its percentage (0.781):
Moles of Boron = (1 mol) * (0.781)
- Multiply the molar mass of Hydrogen by its percentage (0.219):
Moles of Hydrogen = (1 mol) * (0.219)
5. Simplify the ratio of moles of each element to the smallest whole numbers:
- Divide the moles of each element by the smallest number of moles calculated in step 4.
- Round the resulting values to the nearest whole number.
6. Finally, write the molecular formula using the number of atoms of each element obtained in step 5.
Following these steps, you should be able to determine the molecular formula of the unknown gas.
To determine the molecular formula of the unknown gas, we need to calculate the empirical formula of the gas first. The empirical formula gives the simplest whole number ratio of atoms in a compound.
To do this, we will start by finding the number of moles of Boron (B) and Hydrogen (H) in a given mass of the gas.
Step 1: Calculate the number of moles of boron (B)
To find the number of moles of Boron, we will use the percentage composition given. We assume we have 100 grams of the gas, so we have 78.1 grams of Boron in the gas sample.
The molar mass of Boron (B) is 10.81 g/mol, so we can calculate the moles of Boron:
moles of Boron = mass of Boron / molar mass of Boron
moles of Boron = 78.1 g / 10.81 g/mol
Step 2: Calculate the number of moles of hydrogen (H)
To find the number of moles of Hydrogen, we will use the percentage composition given. We assume we have 100 grams of the gas, so we have 21.9 grams of Hydrogen in the gas sample.
The molar mass of Hydrogen (H) is 1.008 g/mol, so we can calculate the moles of Hydrogen:
moles of Hydrogen = mass of Hydrogen / molar mass of Hydrogen
moles of Hydrogen = 21.9 g / 1.008 g/mol
Step 3: Find the simplest whole number ratio
To find the simplest whole number ratio, we divide both the moles of Boron and Hydrogen by the smallest number of moles obtained.
In this case, the smallest number of moles is 2.0203 moles of hydrogen.
So, we divide both moles of Boron and Hydrogen by 2.0203:
moles of Boron (B) = 3.85 moles / 2.0203 = 1.909
moles of Hydrogen (H) = 2.0203 moles / 2.0203 = 1.000
Step 4: Write the empirical formula
The empirical formula is the simplest whole number ratio of atoms. In this case, the moles of Boron and Hydrogen are approximately 1.909 and 1.000, respectively. To simplify the ratio, we round the decimal values to the nearest whole number:
Boron (B) = 2
Hydrogen (H) = 1
Therefore, the empirical formula of the gas is BH2.
Now, we need to find the molecular formula by determining the actual number of atoms present in one molecule of the gas. For this, we need additional information, such as the molar mass of the gas. If you provide the molar mass, I can help you determine the molecular formula.