Final answer:
Using Graham's law and the given effusion rate, it is deduced that the gas with a molar mass of approximately 20.21 g/mol, which is near to neon's atomic mass, is most likely to be the gas in question. Hence, the chemical formula of the gas is Ne.
Step-by-step explanation:
The question relates to effusion rates of gases and employs Graham's law to find the molar mass of an unknown gas. According to Graham's law, the rate of effusion of a gas is inversely proportional to the square root of its molar mass (M). This means that if a gas escapes through a pinhole 1.37 times as fast as F2 gas (with a molar mass of approximately 38 g/mol for F2), we can write the equation:
rate of effusion of A / rate of effusion of B = sqrt(molar mass of B) / sqrt(molar mass of A)
Substituting the given rates and solving for the molar mass of the unknown gas (A), we have:
1.37 = sqrt(38 g/mol) / sqrt(molar mass of A)
We square both sides to get rid of the square root and solve for molar mass of A:
(1.37)^2 = 38 g/mol / molar mass of A
molar mass of A = 38 g/mol / (1.37)^2
molar mass of A ≈ 38 g/mol / 1.88
molar mass of A ≈ 20.21 g/mol
Looking at the periodic table and considering common diatomic gases, the gas that closely matches this molar mass is neon (Ne), with an atomic weight of approximately 20 g/mol. Since the student is asked for a gas made up of atoms, we must consider elemental (monatomic) gases rather than molecular ones.
Therefore, the chemical formula of the gas is Ne.