Let's determine the temperature of the canister using the information provided.
We start with the ideal gas law equation:
[tex]\[ PV = nRT \][/tex]
Where:
- [tex]\( P \)[/tex] is the pressure,
- [tex]\( V \)[/tex] is the volume,
- [tex]\( n \)[/tex] is the number of moles,
- [tex]\( R \)[/tex] is the ideal gas constant,
- and [tex]\( T \)[/tex] is the temperature in Kelvin that we need to find.
Given data:
- Pressure [tex]\( P = 546.8 \)[/tex] kilopascals (kPa)
- Volume [tex]\( V = 75.0 \)[/tex] liters (L)
- Moles [tex]\( n = 15.82 \)[/tex] moles
- Ideal gas constant [tex]\( R = 8.314 \)[/tex] J/(mol·K)
First, convert the pressure from kilopascals to pascals:
[tex]\[ 1 \text{kPa} = 1000 \text{Pa} \][/tex]
[tex]\[ P = 546.8 \text{kPa} \times 1000 = 546800 \text{Pa} \][/tex]
Next, plug the values into the ideal gas law equation and solve for [tex]\( T \)[/tex]:
[tex]\[ T = \frac{PV}{nR} \][/tex]
Substitute the known values:
[tex]\[ T = \frac{546800 \text{ Pa} \times 75.0 \text{ L}}{15.82 \text{ moles} \times 8.314 \text{ J/(mol·K)}} \][/tex]
Calculate:
[tex]\[ T \approx 311797.96 \text{ K} \][/tex]
Express the temperature to three significant figures:
The temperature of the canister is [tex]\( 311797.96 \)[/tex] K
