Question

A neon sign is filled with 1.97 x 10ˆ22 neon atoms. What is the mass (in g) of the gas in this sign?

a) 2.78 g
b) 5.56 g
c) 11.12 g
d) 0.660 g

Answer 1

To calculate the mass of the gas in the neon sign, we need to determine the molar mass of neon and then multiply it by the number of neon atoms in the sign. The mass of the gas in the neon sign is approximately 0.659 g.

Step-by-step explanation:

To calculate the mass of the gas in the neon sign, we need to determine the molar mass of neon and then multiply it by the number of neon atoms in the sign. Neon has three naturally occurring isotopes with different masses: Ne-20, Ne-21, and Ne-22. The molar mass of neon is calculated by multiplying the mass of each isotope by its percent abundance and then summing the values. For example, the molar mass of neon can be calculated as: (0.9048 * 19.992) + (0.0027 * 20.994) + (0.0925 * 21.991) = 20.183 g/mol.

Next, we can use the Avogadro's number (6.022 × 10^23) to convert the number of neon atoms in the sign to moles. The stoichiometry factor is 6.022 × 10^23 atoms of neon = 1 mole of neon. So, the number of moles of neon in the sign is: (1.97 × 10^22 atoms) / (6.022 × 10^23 atoms/mol) = 0.0326 mol.

Finally, we can calculate the mass of the gas in the sign using the molar mass and the number of moles: (0.0326 mol) * (20.183 g/mol) = 0.659 g. Therefore, the mass of the gas in the neon sign is approximately 0.659 g.