Iow many moles of gas are contained in a compressed air tank for scuba diving that has a volume of 6.5 L and a pressure of 230 . atm at 23 . $$ { }^{\circ} \mathrm{C} $$ ? Be sure your nswer has the correct number of significant figures. Note: Reference the Fundamental constants table for additional information.

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To determine the number of moles of gas contained in the compressed air tank, we'll use the **Ideal Gas Law**, which is given by:

$$
PV = nRT
$$

Where:
- $$ P $$ = Pressure (atm)
- $$ V $$ = Volume (L)
- $$ n $$ = Number of moles (mol)
- $$ R $$ = Ideal gas constant ($$0.0821 \, \text{L·atm/mol·K}$$)
- $$ T $$ = Temperature (K)

### Step-by-Step Calculation:

1. **Given Values:**
   - Volume, $$ V = 6.5 \, \text{L} $$ (2 significant figures)
   - Pressure, $$ P = 230 \, \text{atm} $$ (3 significant figures)
   - Temperature, $$ T = 23^\circ \text{C} $$

2. **Convert Temperature to Kelvin:**
   $$
   T(K) = 23 + 273.15 = 296.15 \, \text{K}
   $$

3. **Rearrange the Ideal Gas Law to Solve for $$ n $$:**
   $$
   n = \frac{PV}{RT}
   $$

4. **Plug in the Values:**
   $$
   n = \frac{230 \, \text{atm} \times 6.5 \, \text{L}}{0.0821 \, \text{L·atm/mol·K} \times 296.15 \, \text{K}}
   $$

5. **Calculate the Denominator:**
   $$
   R \times T = 0.0821 \times 296.15 \approx 24.3139 \, \text{L·atm/mol}
   $$

6. **Calculate the Number of Moles:**
   $$
   n = \frac{1495}{24.3139} \approx 61.5 \, \text{mol}
   $$

7. **Determine Significant Figures:**
   - The least number of significant figures in the given values is **2** (from volume and temperature).
   - Therefore, round the answer to **2 significant figures**.

8. **Final Answer:**
   $$
   n \approx 61 \, \text{mol}
   $$

**Final Answer:**  
Approximately 61 mol of gas are contained in the scuba tank.
Approximately 61 mol of gas are in the scuba tank.

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