2 the helium tank has a pressure of 650 torr at 25°C. What will be the pressure if the temperature is tripled?
Answer (2)
[tex]\begin{gathered}\begin{gathered}{\underline{\huge \mathbb{A} {\large \mathrm {NSWER : }}}} \\\end{gathered}\end{gathered}[/tex] To solve this problem, we can use the ideal gas law, which shows the relationship between pressure, volume, temperature, and the number of moles of a gas. However, in this case, we can simplify it using Gay-Lussac's Law, which states that the pressure of a gas is directly proportional to its temperature when the volume is constant. Gay-Lussac's Law: [tex]\frac{P_1}{T_1} = \frac{P_2}{T_2}[/tex] Where: [tex]P_1[/tex] = initial pressure (650 torr)[tex]T_1[/tex] = initial temperature in Kelvin[tex]P_2[/tex] = final pressure [tex]T_2[/tex] = final temperature in Kelvin Convert the initial temperature to Kelvin The initial temperature is given as 25°C. To convert Celsius to Kelvin, we use the formula: [tex]T(K) = T(^\circ C) + 273.15[/tex] So, [tex]T_1 = 25 + 273.15 = 298.15 \text{ K}[/tex] Calculate the final temperature If the temperature is tripled, we calculate [tex]T_2[/tex]: [tex]T_2 = 3 \times T_1 = 3 \times 298.15 = 894.45 \text{ K}[/tex] Use Gay-Lussac's Law to find the final pressure Now we can substitute our values into Gay-Lussac's Law: [tex]\frac{650 \text{ torr}}{298.15 \text{ K}} = \frac{P_2}{894.45 \text{ K}}[/tex] Cross-multiplying gives us: [tex]P_2 = \frac{650 \text{ torr} \times 894.45 \text{ K}}{298.15 \text{ K}}[/tex] Calculate P₂ Calculating this will give: [tex]P_2 = \frac{650 \times 894.45}{298.15} \approx 1,850.83 \text{ torr}[/tex] Conclusion Therefore, if the temperature of the helium tank is tripled, the pressure will be approximately 1,850.83 torr. [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/14/2025 [/tex]
The pressure will be approximately 1950 torr when the temperature is tripled.Key points:Temperature must be in Kelvin for calculations.Pressure increases when temperature increases at constant volume.
