To determine which gas has the higher effusion rate between hydrogen sulfide (H[tex]\(_2\)[/tex]S) and ammonia (NH[tex]\(_3\)[/tex]), we can use Graham's law of effusion. Graham's law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. This can be mathematically expressed as follows:
[tex]\[ \text{Rate of effusion} \propto \frac{1}{\sqrt{M}} \][/tex]
where [tex]\( M \)[/tex] is the molar mass of the gas.
First, let's identify the molar masses of the two gases:
- Molar mass of [tex]\( H_2S \)[/tex] is approximately 34.08 grams per mole.
- Molar mass of [tex]\( NH_3 \)[/tex] is approximately 17.03 grams per mole.
Next, we calculate the effusion rates for each gas using the inverse square root of their molar masses:
1. For [tex]\( H_2S \)[/tex]:
[tex]\[ \text{Rate of effusion of } H_2S = \frac{1}{\sqrt{34.08}} \approx 0.1713 \][/tex]
2. For [tex]\( NH_3 \)[/tex]:
[tex]\[ \text{Rate of effusion of } NH_3 = \frac{1}{\sqrt{17.03}} \approx 0.2423 \][/tex]
Now, let's compare the calculated effusion rates:
- Effusion rate of [tex]\( H_2S \)[/tex] [tex]\(\approx 0.1713\)[/tex]
- Effusion rate of [tex]\( NH_3 \)[/tex] [tex]\(\approx 0.2423\)[/tex]
Since 0.2423 (effusion rate of [tex]\( NH_3 \)[/tex]) is greater than 0.1713 (effusion rate of [tex]\( H_2S \)[/tex]), we can conclude that:
Ammonia (NH[tex]\(_3\)[/tex]) has the higher effusion rate.
