a sample of lead glass is prepared by melting together 20.0 g og silica (SiO2), and 80.0 g of lead oxide (PbO). what is the mole fraction of SiO2 and PbO in the glass?
Calculate molar mass for SiO2 and PbO
Calculate the number of moles of each material in 20.0 g of silica (SiO2), and 80.0 g of lead oxide (PbO).
number of moles = mass/molar mass
Calculate the mole fraction
mole fraction of SiO2=
number of moles of SiO2/total moles
0.482
To determine the mole fraction of SiO2 and PbO in the glass, we need to calculate the moles of SiO2 and PbO first.
First, we calculate the moles of SiO2:
Molar mass of SiO2 = 28.0855 g/mol + 15.9994 g/mol = 60.0849 g/mol
Moles of SiO2 = mass of SiO2 / molar mass of SiO2
Moles of SiO2 = 20.0 g / 60.0849 g/mol
Next, we calculate the moles of PbO:
Molar mass of PbO = 207.2 g/mol + 15.9994 g/mol = 223.1994 g/mol
Moles of PbO = mass of PbO / molar mass of PbO
Moles of PbO = 80.0 g / 223.1994 g/mol
Now, we can calculate the mole fraction of SiO2 and PbO:
Mole fraction of SiO2 = moles of SiO2 / (moles of SiO2 + moles of PbO)
Mole fraction of PbO = moles of PbO / (moles of SiO2 + moles of PbO)
Substituting the values:
Mole fraction of SiO2 = (20.0 g / 60.084 g/mol) / [(20.0 g / 60.084 g/mol) + (80.0 g / 223.199 g/mol)]
Mole fraction of PbO = (80.0 g / 223.199 g/mol) / [(20.0 g / 60.084 g/mol) + (80.0 g / 223.199 g/mol)]
Calculating the values:
Mole fraction of SiO2 ≈ 0.253
Mole fraction of PbO ≈ 0.747
Therefore, the mole fraction of SiO2 in the glass is approximately 0.253, and the mole fraction of PbO is approximately 0.747.
To find the mole fraction of each component in the lead glass, we need to calculate the number of moles of each substance.
Step 1: Calculate the number of moles of SiO2 (silica).
The molar mass of SiO2 is 28.08 g/mol + 16.00 g/mol = 44.08 g/mol.
Number of moles of SiO2 = Mass of SiO2 / Molar mass of SiO2
= 20.0 g / 44.08 g/mol
≈ 0.453 mol
Step 2: Calculate the number of moles of PbO (lead oxide).
The molar mass of PbO is 207.2 g/mol + 16.00 g/mol = 223.2 g/mol.
Number of moles of PbO = Mass of PbO / Molar mass of PbO
= 80.0 g / 223.2 g/mol
≈ 0.358 mol
Step 3: Calculate the sum of the moles of both components.
Total moles = Number of moles of SiO2 + Number of moles of PbO
= 0.453 mol + 0.358 mol
≈ 0.811 mol
Step 4: Calculate the mole fraction of each component.
Mole fraction of SiO2 = Number of moles of SiO2 / Total moles
= 0.453 mol / 0.811 mol
≈ 0.558
Mole fraction of PbO = Number of moles of PbO / Total moles
= 0.358 mol / 0.811 mol
≈ 0.442
Therefore, the mole fraction of SiO2 in the lead glass is approximately 0.558, and the mole fraction of PbO is approximately 0.442.