How 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 answer has the correct number of significant figures. Note: Reference the Fundamental constants table for additional information.

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To find the number of moles of gas in the scuba diving tank, we can use the Ideal Gas Law, which is given by the equation:

$$
PV = nRT
$$

Where:
- $$ P $$ = pressure (in atm)
- $$ V $$ = volume (in liters)
- $$ n $$ = number of moles
- $$ R $$ = ideal gas constant (0.0821 L·atm/(K·mol))
- $$ T $$ = temperature (in Kelvin)

### Step 1: Convert the temperature to Kelvin
The temperature in Celsius can be converted to Kelvin using the formula:

$$
T(K) = T(°C) + 273.15
$$

Given $$ T = 23 \, °C $$:

$$
T = 23 + 273.15 = 296.15 \, K
$$

### Step 2: Substitute the known values into the Ideal Gas Law
We have:
- $$ P = 230 \, atm $$
- $$ V = 6.5 \, L $$
- $$ R = 0.0821 \, L·atm/(K·mol) $$
- $$ T = 296.15 \, K $$

Now we can rearrange the Ideal Gas Law to solve for $$ n $$:

$$
n = \frac{PV}{RT}
$$

### Step 3: Calculate the number of moles
Substituting the values into the equation:

$$
n = \frac{(230 \, atm)(6.5 \, L)}{(0.0821 \, L·atm/(K·mol))(296.15 \, K)}
$$

Now, let's perform the calculation.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\left(230\times 6.5\right)}{\left(0.0821\times 296.15\right)}$$
- step1: Remove the parentheses:
  $$\frac{230\times 6.5}{0.0821\times 296.15}$$
- step2: Multiply the numbers:
  $$\frac{1495}{0.0821\times 296.15}$$
- step3: Multiply the numbers:
  $$\frac{1495}{24.313915}$$
- step4: Convert the expressions:
  $$\frac{1495}{\frac{4862783}{200000}}$$
- step5: Multiply by the reciprocal:
  $$1495\times \frac{200000}{4862783}$$
- step6: Multiply:
  $$\frac{1495\times 200000}{4862783}$$
- step7: Multiply:
  $$\frac{299000000}{4862783}$$
Calculating the number of moles:

$$
n \approx \frac{1495}{24.475} \approx 61.49
$$

### Step 4: Determine significant figures
The values provided have the following significant figures:
- Volume (6.5 L) has 2 significant figures.
- Pressure (230 atm) has 2 significant figures.
- Temperature (23 °C) has 2 significant figures.

Thus, the final answer should also be reported with 2 significant figures.

### Final Answer
The number of moles of gas in the compressed air tank is:

$$
n \approx 61 \, \text{moles}
$$
There are approximately 61 moles of gas in the scuba diving tank.

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