Final answer:
The number of moles of gas A and B must be equal to have the same internal energy (1:1), and since 1.0 g of A is equivalent in internal energy to 0.10 g of B, the atomic mass of A must be ten times that of B (10:1). The correct answer is (a) (a) 1:1, (b) 10:1.
Step-by-step explanation:
The problem is based on comparing the internal energies of two monatomic ideal gases at the same temperature. Since both gases are at the same temperature and are monatomic, their internal energies per mole are the same, due to each mole having the same degree of freedom (3/2)RT, where R is the gas constant and T is the temperature. We are given that 1.0 g of gas A has the same internal energy as 0.10 g of gas B.
For part (a), since the internal energy is the same and depends on the number of moles and temperature, we can say that the number of moles must be equal for equal amounts of internal energy. Therefore, if we have ten times less mass for gas B to have the same energy, gas B must have ten times more moles per gram than gas A. Thus, the ratio of the number of moles of each gas is 1:1.
For part (b), the ratio of the atomic masses can be deduced from the masses given and the equality of moles. Since 1.0 g of A has the same number of moles as 0.10 g of B, molecular weight A must be ten times that of B to compensate for the larger mass. Therefore, the ratio of the atomic masses of the two gases is 10:1.
The correct answer to the question would be option (a) (a) 1:1, (b) 10:1.