Gas Laws Fact Sheet

\begin{tabular}{|c|c|}
\hline Ideal gas law & [tex]$P V = n R T$[/tex] \\
\hline Ideal gas constant & \begin{tabular}{l}
[tex]$R = 8.314 \frac{L \cdot kPa}{mol \cdot K}$[/tex] \\
or \\
[tex]$R = 0.0821 \frac{L \cdot atm}{mol \cdot K}$[/tex]
\end{tabular} \\
\hline Standard atmospheric pressure & [tex]$1 atm = 101.3 kPa$[/tex] \\
\hline Celsius to Kelvin conversion & [tex]$K = ^{\circ}C + 273.15$[/tex] \\
\hline
\end{tabular}

Type the correct answer in the box. Express your answer to three significant figures.

A 75.0-milliliter lightbulb is filled with neon. There are [tex]$7.16 \times 10^{-4}$[/tex] moles of gas in it, and the absolute pressure is 116.8 kilopascals after the bulb has been on for an hour. How hot did the bulb get?

The temperature of the lightbulb was [tex]$\square$[/tex] K



Answer :

Let's solve the problem step-by-step using the provided information:

1. Given Data:
- Volume of the lightbulb, [tex]\( V = 75.0 \)[/tex] milliliters
- Moles of neon gas, [tex]\( n = 7.16 \times 10^{-4} \)[/tex] moles
- Absolute pressure, [tex]\( P = 116.8 \)[/tex] kilopascals (kPa)
- Ideal gas constant, [tex]\( R = 8.314 \frac{ L \cdot kPa }{ mol \cdot K} \)[/tex]
- Standard atmospheric pressure, [tex]\( 1 \)[/tex] atm [tex]\( = 101.3 \)[/tex] kPa

2. Convert the volume from milliliters to liters:
[tex]\[ V = 75.0 \text{ mL} \times \frac{1 \text{ L}}{1000 \text{ mL}} = 0.0750 \text{ L} \][/tex]

3. Convert pressure from kilopascals to atmospheres:
[tex]\[ P_{atm} = \frac{116.8 \text{ kPa}}{101.3 \text{ kPa/atm}} \approx 1.153 \text{ atm} \][/tex]

4. Use the Ideal Gas Law [tex]\((PV = nRT)\)[/tex] to solve for the temperature [tex]\(T\)[/tex]:
[tex]\[ T = \frac{PV}{nR} \][/tex]
Substituting in the values, we get:
[tex]\[ T = \frac{(1.153 \text{ atm}) \times (0.0750 \text{ L})}{(7.16 \times 10^{-4} \text{ moles}) \times (0.0821 \frac{L \cdot atm}{mol \cdot K})} \][/tex]

5. Perform the calculation:
[tex]\[ T = \frac{0.086475 \text{ L} \cdot \text{ atm}}{0.000058828 \text{ L} \cdot \text{ atm} / \text{ K}} \][/tex]
[tex]\[ T \approx 14.527 \text{ K} \][/tex]

Expressing the final temperature to three significant figures:

The temperature of the lightbulb was [tex]\(\boxed{14.5} \text{ K}\)[/tex]