\(500cm^{-3}\) 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...

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: \(\frac{72\times500}{76}cm^3\)