\(500cm^{-3}\) of a gas is collected at 0°C and at a pressure of 72cm of mercury. What is the volume of the the gas at the same temperature and at a pressur...
Question 1 Report
\(500cm^{-3}\) of a gas is collected at 0°C and at a pressure of 72cm of mercury. What is the volume of the the gas at the same temperature and at a pressure of 76cm of the same mercury?
Answer Details
The relationship between the pressure and volume of a gas is given by the Boyle's Law, which states that at constant temperature, the pressure and volume of a gas are inversely proportional to each other. This means that if the pressure of a gas increases, its volume decreases and vice versa.
Using the Boyle's Law, we can solve the problem as follows:
Let V be the volume of the gas at a pressure of 76 cm of mercury.
Using Boyle's Law, we have:
P₁V₁ = P₂V₂
where P₁ and V₁ are the initial pressure and volume of the gas, respectively, and P₂ and V₂ are the final pressure and volume of the gas, respectively.
Substituting the given values, we get:
(72 cm)(500 cm³) = (76 cm)(V₂)
Solving for V₂, we have:
V₂ = (72 cm)(500 cm³) / (76 cm)
V₂ = 459.21 cm³ (rounded to two decimal places)
Therefore, the volume of the gas at the same temperature and at a pressure of 76 cm of the same mercury is approximately 459.21 cm³.
Answer: \(\frac{72\times500}{76}cm^3\)
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