Question 1: A container holds 20.0L to an unknown sample of gas at 288.15K. What will be its new volume if the temperature increases by 308.15K?
Answer (1)
[tex]\begin{gathered}\begin{gathered}{\underline{\huge \mathbb{A} {\large \mathrm {NSWER : }}}} \\\end{gathered}\end{gathered}[/tex] Problem: A gas sample occupies a volume of 20.0 L at a temperature of 288.15 K. What will be the new volume of the gas if the temperature is increased by 308.15 K? Solution: Understanding the Concept: Charles's Law: This law states that the volume of a gas is directly proportional to its absolute temperature, assuming the pressure is constant. This means as the temperature goes up, the volume of the gas increases proportionally. The Formula: Charles's Law can be expressed as: [tex]\frac{V_1}{T_1} = \frac{V_2}{T_2}[/tex] where: V₁ = Initial volume T₁ = Initial temperature (in Kelvin)V₂ = Final volumeT₂ = Final temperature (in Kelvin) Calculation: Identify the knowns and unknowns: V₁ = 20.0 LT₁ = 288.15 KT₂ = 288.15 K + 308.15 K = 596.3 K V₂ = ? Rearrange Charles's Law to solve for the unknown (V₂): [tex]V_2 = \frac{V_1 \times T_2}{T_1}[/tex] Substitute the known values into the equation: [tex]V_2 = \frac{20.0 \text{ L} \times 596.3 \text{ K}}{288.15 \text{ K}}[/tex] Calculate V₂: [tex]V_2 = 41.4 \text{ L} \text{ (approximately)}[/tex] Answer: The new volume of the gas will be approximately 41.4 L if the temperature increases by 308.15 K. Important Notes: Make sure to use Kelvin (K) for temperature in the calculations.Always use the correct formula and plug in the values carefully. Real-World Application: Charles's Law explains how hot air balloons rise. As the air inside the balloon is heated, its volume increases, making the balloon less dense than the surrounding air, causing it to rise. [tex]\sf\color{green}{⊱⋅ ────────────────────── ⋅⊰}[/tex][tex]\begin{gathered} \boxed{\begin{array}{cc} \sf \footnotesize \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ···\: ʚ\: \: \: \: \: \: Hope\:it\:helps \: \: \: \: \: ɞ \:··· \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf\footnotesize\:\# CarryOnLearning \\ \sf\footnotesize ૮₍´˶ \: • \: . \: • \: ⑅ ₎ა \: \leadsto \footnotesize\sf\color{purple} \underline{Study\:Well!}\end{array}}\end{gathered}[/tex][tex]\sf\color{green}{⊱⋅ ────────────────────── ⋅⊰}[/tex][tex]\large\qquad\qquad\qquad\tt MARCH/16/2025 [/tex]
