Question

Neon gas was heated from 50oC to 150oC. Its new volume is 175 mL. What was the original volume?

Answer 1

Charles's Law-

`\:\:\:\:\:\: \:\:\:\:\:\:\star\longrightarrow\sf \underline{(V_1)/(T_1)=(V_2)/(T_2)}\\`

Where:-

• V₁ = Initial volume
• T₁ = Initial temperature
• V₂ = Final volume
• T₂ = Final temperature

As per question, we are given that -

• V₂ =175 mL
• T₁ = 50°C
• T₂ = 150°C

We are given the initial temperature and the final temperature in °C.So, we first have to convert those temperatures in Celsius to kelvin by adding 273-

`\:\:\:\:\:\:\star\sf T_1` = 50+ 273 = 323K

`\:\:\:\:\:\:\star\sf T_2` =150+273 = 423K

Now that we have obtained all the required values, so we can put them into the formula and solve for V₁:-

`\:\:\:\:\:\: \:\:\:\:\:\:\star\longrightarrow\sf \underline{(V_1)/(T_1)=(V_2)/(T_2)}\\`

`\:\:\:\:\:\:\:\:\:\:\:\:\longrightarrow \sf V_1 = (V_2)/(T_2)* T_1\\`

`\:\:\:\:\:\:\:\:\:\:\:\:\longrightarrow \sf V_1 = (175)/(423)* 323\\`

`\:\:\:\:\:\:\:\:\:\:\:\:\longrightarrow \sf V_1 = 0.41371......* 323\\`

`\:\:\:\:\:\: \:\:\:\:\:\:\longrightarrow \sf V_1 = 133.628........\\`

`\:\:\:\:\:\:\:\:\:\:\:\:\longrightarrow \sf\underline{ V_1 = 133.63 mL}\\`

Therefore, the original volume ( Initial volume) of neon is 133.63mL.