Question

40 ml of ammonia gas taken in an eudiometer tube was subjected to sparks till the volume did not change any further . The volume was found to increase by 40 ml . 40 ml of oxygen was then mixed and the mixture was further exploded . the gases remained were 30 ml . deduce the formula of ammonia .solve it , with solution

Answer 1

Answer : The formula of ammonia is NH₃

Explanation :

We know that the ammonia gas is made by combination of nitrogen N and hydrogen H.

Let us assume the formula of ammonia is $N_{x}H_{y}$

When the gas is subjected to sparks, it decomposes into its elemental gases N₂ and H₂. The balanced equation for this reaction can be written as

$N_{x}H_{y} \rightarrow\frac{x}{2} N_{2} +\frac{y}{2} H_{2}$

The initial volume of the gas is 40 mL and we know that the volume increases by 40 mL. That means the final volume occupied by N₂ and H₂ in eudiometer is 40 mL + 40  mL = 80 mL.

Please  take a look at the ICE table 1.

From the ICE table we know that, after the reaction is complete we get 20x mL of N₂ and 20y mL of H₂.

The total volume of N₂ and H₂ is 80 mL.

Therefore we have,

$20x + 20y =80$

$x+y =\frac{80}{20}$

$x+y=4$ ..........Equation 1

After the decomposition reaction is complete, we get N₂ and H₂. This mixture is further exploded with oxygen. Nitrogen being inert to reaction with oxygen remains as it is.

The reaction of hydrogen with oxygen creates liquid water which is no more in the gas form. This reaction removes hydrogen gas completely from the mixture.

Therefore the final reaction mixture contains unreacted N₂ and excess oxygen.

Let us set up another ICE table to find out the final amount O₂.

Please refer to ICE table 2

From the ICE we know that volume of O₂ that is left is (40-10y) L and from previous ICE table we have volume of N₂ as 20x mL.

The final volume of reaction mixture is 30 mL.

Therefore we have,

$40-10y+20x = 30$

On further simplification we get

$20x-10y=30-40$

$20x-10y=-10$

Divide the entire equation by 10

$2x-y=-1$ ..............Equation 2

Let us add equation 1 and 2

 $x+y=4$

+ $2x-y=-1$

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$3x = 3$

$x=1$

Let us plug in this value of x in equation 1

$x+y = 4$

$1+y = 4$

$y=3$

But we have the formula of ammonia as $N_{x}H_{y}$

Let us plug in the values of x and y

The formula of ammonia is N₁H₃ which is NH₃