Question

Equal volumes of ammonia gas and chlorine gas are kept in two different containers under the same conditions of temperature and pressure. Find the number of molecules contained in chlorine gas when the mass of ammonia is 34 g. (Atomic weight: Cl = 35.5, H = 1, N = 14)

Hint:

You don't actually need the atomic weight of Chlorine for this specific problem because Avogadro's Law links volume directly to the number of molecules, regardless of the gas's identity!

Answer 1

Step 1: Apply Avogadro's Law:
Avogadro's Law states that equal volumes of all gases, under the same conditions of temperature and pressure, contain an equal number of molecules (and thus an equal number of moles). [ textMoles of NH_3 = textMoles of Cl_2 ] Step 2: Calculate moles of Ammonia ((NH_3)):
Molecular weight of (NH_3 = 14 + (1 times 3) = 17) g/mol. [ textMoles = fractextMasstextMolar Mass = frac34text g17text g/mol = 2text moles ] Step 3: Determine molecules in Chlorine ((Cl_2)):
Since the volumes are equal, Chlorine also has 2 moles. [ textNumber of molecules = textMoles times textAvogadro's Number (N_A) ] [ textNumber of molecules = 2 times 6.022 times 10^23 = 1.2044 times 10^24 text molecules ] Final Answer: The chlorine gas contains (1.2044 times 10^24) molecules (or simply (2N_A) molecules).