Question
2. A sample of carbon dioxide is placed in a piston. The initial temperature of the gas is 35^circ C and it occupies a volume of 2.2 L . Calculate the temperature at which it will occupy 4.4 L . Pressure and the amount of gas remain constant. [ans: 620K]
Solution
4.7
(215 Votes)
Justin
Master · Tutor for 5 years
Answer
Here's how to solve this problem using Charles's Law:**1. Charles's Law:**Charles's Law states that the volume of a gas is directly proportional to its absolute temperature when the pressure and the amount of gas are held constant. Mathematically, this is expressed as:V₁/T₁ = V₂/T₂Where:* V₁ = Initial volume* T₁ = Initial temperature (in Kelvin)* V₂ = Final volume* T₂ = Final temperature (in Kelvin)**2. Convert Celsius to Kelvin:**Temperatures must be in Kelvin for gas law calculations. To convert Celsius to Kelvin, add 273.15:T₁ = 35°C + 273.15 = 308.15 K**3. Solve for T₂:**We are given:* V₁ = 2.2 L* T₁ = 308.15 K* V₂ = 4.4 LWe need to find T₂. Rearrange Charles's Law to solve for T₂:T₂ = (V₂ * T₁) / V₁T₂ = (4.4 L * 308.15 K) / 2.2 LT₂ = 616.3 K**4. Round to Significant Figures:**The initial temperature (35°C) has two significant figures. Therefore, we should round our answer to two significant figures:T₂ ≈ 620 KTherefore, the temperature at which the carbon dioxide will occupy 4.4 L is approximately 620 K.