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

Since the gases are kept under the same conditions of temperature and pressure and they occupy equal volumes, we use Avogadro’s law.

Avogadro’s law:
Equal volumes of all gases, under the same conditions of temperature and pressure, contain equal number of molecules.

So, the number of molecules in ammonia gas = the number of molecules in chlorine gas.

Step 1: Find the molar mass of ammonia (NH₃)
Atomic mass of N = 14
Atomic mass of H = 1

Molar mass of NH₃ = 14 + (3 × 1) = 17 g/mol

Step 2: Find the number of moles in 34 g of ammonia
\[ \text{Number of moles of NH}_3 = \frac{34}{17} = 2 \] So, 34 g of ammonia = 2 moles of NH₃.

Step 3: Find the number of molecules in 2 moles of ammonia
1 mole of any substance contains 6.023 × 10²³ molecules.

Therefore,

\[ \text{Number of molecules in 2 moles} = 2 \times 6.023 \times 10^{23} \] \[ = 1.2046 \times 10^{24} \]
Since chlorine gas has equal volume under the same conditions, it will also contain the same number of molecules.

Final Answer:
\[ \boxed{1.2046 \times 10^{24} \text{ molecules}} \]
Therefore, the number of molecules present in chlorine gas is 1.2046 × 10²⁴.