Sure, let's solve this problem step-by-step using the ideal gas law [tex]\( PV = nRT \)[/tex].
### Step 1: Write down the given values:
- Number of moles ([tex]\( n \)[/tex]): 0.750 mol
- Volume ([tex]\( V \)[/tex]): 6850 mL
- Pressure ([tex]\( P \)[/tex]): 2.21 atm
- Gas constant ([tex]\( R \)[/tex]): [tex]\( 0.0821 \frac{L \cdot atm}{mol \cdot K} \)[/tex]
### Step 2: Convert the volume from milliliters to liters:
Since [tex]\( 1 \, \text{L} = 1000 \, \text{mL} \)[/tex],
[tex]\[ V = \frac{6850 \, \text{mL}}{1000} = 6.85 \, \text{L} \][/tex]
### Step 3: Rearrange the ideal gas law to solve for temperature ([tex]\( T \)[/tex]):
The ideal gas law is [tex]\( PV = nRT \)[/tex].
Rearranging it to solve for [tex]\( T \)[/tex]:
[tex]\[ T = \frac{PV}{nR} \][/tex]
### Step 4: Plug in the known values:
[tex]\[ P = 2.21 \, \text{atm} \][/tex]
[tex]\[ V = 6.85 \, \text{L} \][/tex]
[tex]\[ n = 0.750 \, \text{mol} \][/tex]
[tex]\[ R = 0.0821 \frac{L \cdot atm}{mol \cdot K} \][/tex]
### Step 5: Calculate the temperature:
[tex]\[ T = \frac{(2.21 \, \text{atm}) \times (6.85 \, \text{L})}{(0.750 \, \text{mol}) \times (0.0821 \frac{L \cdot atm}{mol \cdot K})} \][/tex]
### Step 6: Perform the multiplication and division to find [tex]\( T \)[/tex]:
[tex]\[ T = \frac{15.1385 \, \text{atm} \cdot \text{L}}{0.061575 \, \text{mol} \cdot \frac{L \cdot atm}{mol \cdot K}} \][/tex]
[tex]\[ T = 245.8546488022736 \, K \][/tex]
So, the temperature of the gas is approximately 246 K.
Hence, the correct answer is:
246 K
