Which of the following gases occupy the smallest volume at STP?
a) 1.000 mol carbon dioxide
b) 4.032 g H2
c) 35.45 g Cl2
d) 6.022 x 10^23 molecules of O2
Why not just calculate the volume of each?
mols = grams/molar mass
mols = molecules/6.022E23
Use PV = nRT
To determine which gas occupies the smallest volume at STP (Standard Temperature and Pressure), we need to compare the number of moles of each gas. Using Avogadro's Law, we know that equal volumes of gases at the same temperature and pressure contain an equal number of molecules or moles.
Let's calculate the number of moles for each gas:
a) For 1.000 mol of carbon dioxide (CO2), the number of moles is already given as 1.000 mol.
b) To calculate the number of moles for 4.032 g of hydrogen gas (H2), we need to use the molar mass of hydrogen. The molar mass of hydrogen is 2.016 g/mol (1 g/mol for each hydrogen atom). We can calculate the number of moles using the formula:
Number of moles = Mass / Molar mass
Number of moles = 4.032 g / 2.016 g/mol = 2.00 mol
c) To calculate the number of moles for 35.45 g of chlorine gas (Cl2), we need to use the molar mass of chlorine. The molar mass of chlorine is 35.45 g/mol (17.45 g/mol for each chlorine atom). We can calculate the number of moles using the formula:
Number of moles = Mass / Molar mass
Number of moles = 35.45 g / 35.45 g/mol = 1.00 mol
d) For 6.022 x 10^23 molecules of oxygen gas (O2), we need to convert the number of molecules to moles. Avogadro's number states that 1 mole of any substance contains 6.022 x 10^23 particles (atoms, molecules, etc.). Since we have 6.022 x 10^23 molecules of O2, we have:
Number of moles = Number of molecules / Avogadro's number
Number of moles = 6.022 x 10^23 / (6.022 x 10^23/mol) = 1.00 mol
Comparing the number of moles for each gas, we see that all gases occupy the same volume at STP. Therefore, the gases in options a), b), c), and d) all occupy the same volume at STP.