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A sample of a gas occupies 223 mL at 57.0°C and a pressure of 193.0 torr. What is the temperature in degrees Celsius (°C) of the gas when it is placed in a 313 mL flask at a pressure of 264.5 torr?

Answer :

Final answer:

According to Charles's law, the temperature of the gas when placed in a larger flask at a different pressure can be calculated using the formula T₂ = (V₂ / V₁) × T₁. By substituting the given values, we find that the temperature is approximately 188.98 °C.

Explanation:

The question is asking for the temperature in degrees Celsius (°C) of a gas that is placed in a larger flask at a different pressure. We can use Charles's law to solve this problem. Charles's law states that at constant pressure, the volume of a gas is directly proportional to its temperature in Kelvin (K). The formula for Charles's law is V₁/T₁ = V₂/T₂, where V₁ and T₁ are the initial volume and temperature, and V₂ and T₂ are the final volume and temperature. By rearranging this formula, we can solve for T₂. Let's plug in the given values: V₁ = 223 ml, T₁ = 57.0°C, P₁ = 193.0 torr, V₂ = 313 ml, and P₂ = 264.5 torr. Converting the temperatures to Kelvin, we have T₁ = 57.0 + 273.15 = 330.15 K and T₂. Solving for T₂, we get:

T₂ = (V₂ / V₁) × T₁

T₂ = (313 ml / 223 ml) × 330.15 K

T₂ ≈ 462.13 K

Converting the temperature back to Celsius, we have T₂ ≈ 462.13 - 273.15 ≈ 188.98 °C

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