Question

consider the true analogy showing the relationship between amu and grams.
amu : particle :: grams : mole
which choice shows an incorrect analogy?

1. (mg) 24.305 amu : atom :: 24.305 g : mole
2. (k) 39.10 amu : atom :: 39.10 g : mole
3. (ni) 59 amu : atom :: 58.69 g : mole
4. (br₂) 159.8 amu : molecule :: 159.8 g : mole

Explanation:

Step1: Recall the relationship

The analogy given is \( \text{amu} : \text{particle} :: \text{grams} : \text{mole} \). For an element, the atomic mass in amu (atomic mass unit) per atom should be equal to the molar mass in grams per mole. This is because 1 mole of a substance contains Avogadro's number of particles, and the mass in grams of 1 mole (molar mass) is numerically equal to the atomic mass in amu of one atom (or molecular mass in amu of one molecule for compounds).

Step2: Analyze each option

• Option 1 (Mg): Atomic mass of Mg is 24.305 amu per atom. Molar mass should be 24.305 g per mole. This follows the analogy.
• Option 2 (K): Atomic mass of K is 39.10 amu per atom. Molar mass should be 39.10 g per mole. This follows the analogy.
• Option 3 (Ni): Atomic mass of Ni is approximately 58.69 amu per atom (not 59). So the analogy here has 59 amu per atom vs 58.69 g per mole, which does not match. The amu value and gram value should be numerically equal.
• Option 4 (\( \text{Br}_2 \)): Molecular mass of \( \text{Br}_2 \) is \( 2\times79.90 = 159.8 \) amu per molecule. Molar mass should be 159.8 g per mole. This follows the analogy.

Answer:

1. (Ni) 59 amu : atom :: 58.69 g : mole