Agas has a pressure of 2.0 atm a volume of 4.0 L, and a temperature of 300 K. How many moles of gas are present? Use R=0.0821Lcdot atm/(molcdot K) Desmos scientific calculator 0.16 mol 0.33 mol 0.74 mol 0.54 mol

To solve this problem, we will use the **Ideal Gas Law**:<br /><br />\[<br />PV = nRT<br />\]<br /><br />Where: <br />- \( P \) is the pressure (in atm) <br />- \( V \) is the volume (in liters) <br />- \( n \) is the number of moles (what we are solving for) <br />- \( R \) is the ideal gas constant (\( 0.0821 \, \text{L·atm/(mol·K)} \)) <br />- \( T \) is the temperature (in Kelvin)<br /><br />### Step 1: Rearrange the formula to solve for \( n \):<br />\[<br />n = \frac{PV}{RT}<br />\]<br /><br />### Step 2: Substitute the given values:<br />- \( P = 2.0 \, \text{atm} \)<br />- \( V = 4.0 \, \text{L} \)<br />- \( R = 0.0821 \, \text{L·atm/(mol·K)} \)<br />- \( T = 300 \, \text{K} \)<br /><br />\[<br />n = \frac{(2.0)(4.0)}{(0.0821)(300)}<br />\]<br /><br />### Step 3: Perform the calculations:<br />1. Multiply \( P \) and \( V \): <br /> \[<br /> 2.0 \times 4.0 = 8.0<br /> \]<br /><br />2. Multiply \( R \) and \( T \): <br /> \[<br /> 0.0821 \times 300 = 24.63<br /> \]<br /><br />3. Divide \( PV \) by \( RT \): <br /> \[<br /> n = \frac{8.0}{24.63} \approx 0.325<br /> \]<br /><br />### Step 4: Round to two decimal places:<br />\[<br />n \approx 0.33 \, \text{mol}<br />\]<br /><br />### Final Answer:<br />The number of moles of gas present is **0.33 mol**.<br /><br />Correct option: **0.33 mol**