QJEEM23Cha0ef: JEE Main 2023 Chemistry - Class 11 JEEM23Cha0ef Solution: At constant temperature, a gas is at a pressure of 940.3 mm Hg. …
At constant temperature, a gas is at a pressure of 940.3 mm Hg. The pressure at which its volume decreases by 40% is __________ mm Hg. (Nearest integer)
Step-by-Step Verified Solution
To find the pressure at which the volume decreases by 40%, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at constant temperature.
Let's assume the initial volume of the gas is V. According to Boyle's Law:
P₁V₁ = P₂V₂
Where P₁ is the initial pressure (940.3 mm Hg), V₁ is the initial volume, P₂ is the final pressure (which we need to find), and V₂ is the final volume (which is 40% less than the initial volume, or 0.6V).
Plugging in the values, we have:
940.3 mm Hg × V₁ = P₂ × (0.6V)
Now we can solve for P₂:
P₂ = (940.3 mm Hg × V₁) / (0.6V)
Since the question does not provide the initial volume (V₁), we cannot calculate the exact pressure. However, we can determine the pressure ratio when the volume decreases by 40%.
P₂ = (940.3 mm Hg × V₁) / (0.6V)
We can simplify this by canceling out V:
P₂ = 940.3 mm Hg / 0.6
P₂ ≈ 1567 mm Hg (nearest integer)
Therefore, the pressure at which the volume decreases by 40% is approximately 1567 mm Hg.