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]

Here's how to solve this problem using Charles's Law:<br /><br />**1. Charles's Law:**<br /><br />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:<br /><br />V₁/T₁ = V₂/T₂<br /><br />Where:<br /><br />* V₁ = Initial volume<br />* T₁ = Initial temperature (in Kelvin)<br />* V₂ = Final volume<br />* T₂ = Final temperature (in Kelvin)<br /><br />**2. Convert Celsius to Kelvin:**<br /><br />Temperatures must be in Kelvin for gas law calculations. To convert Celsius to Kelvin, add 273.15:<br /><br />T₁ = 35°C + 273.15 = 308.15 K<br /><br />**3. Solve for T₂:**<br /><br />We are given:<br /><br />* V₁ = 2.2 L<br />* T₁ = 308.15 K<br />* V₂ = 4.4 L<br /><br />We need to find T₂. Rearrange Charles's Law to solve for T₂:<br /><br />T₂ = (V₂ * T₁) / V₁<br /><br />T₂ = (4.4 L * 308.15 K) / 2.2 L<br /><br />T₂ = 616.3 K<br /><br />**4. Round to Significant Figures:**<br /><br />The initial temperature (35°C) has two significant figures. Therefore, we should round our answer to two significant figures:<br /><br />T₂ ≈ 620 K<br /><br />Therefore, the temperature at which the carbon dioxide will occupy 4.4 L is approximately 620 K.<br />