If an aqueous solution is very dilute, will its molality be greater than its molarity, nearly the same as its molarity, or smaller than its molarity?

Molality stays nearly the same as its molarity

Explanation:

Let's make an example of this:

An aqueous solution of 1 mol of NaCl is diluited in a volume of 1L (A).

The same solution is diluited in a volume of 1L, but now we have 0.00001 moles of NaCl (B)

Solution A → Concentrated, [NaCl] = 1 M, 1 m

1L = 1kg

Solution B → Diluted, less concentration, Less molarity and molality.

Now, solution B has a volume of 5L, with 2 moles of solute while A, stays the same.

Molarity A = 1M

Molality A = 1m

Molarity B = 0.4 M

Molality B = 0.4 m

In conclussion, stays nearly the same as its molarity