Question

How many moles of propane gas are in a 70.0 L tank at 20°C and 8.45 atm of pressure?
a
0.629 mol
b
23.2 mol
c
24.6 mol
d
1.59 mol

Answer 1

To determine the number of moles of propane gas in the tank, we can use the Ideal Gas Law, which is expressed as:

\[
PV = nRT
\]

Where:
- \(P\) = pressure in atmospheres (atm)
- \(V\) = volume in liters (L)
- \(n\) = number of moles (mol)
- \(R\) = ideal gas constant (\(0.0821 \, \text{L} \cdot \text{atm} / \text{mol} \cdot \text{K}\))
- \(T\) = temperature in Kelvin (K)

### Step 1: Convert the temperature to Kelvin
The temperature in Celsius is given as 20°C. We convert this to Kelvin using the formula:

\[
T(K) = T(°C) + 273.15
\]

So,

\[
T = 20 + 273.15 = 293.15 \, K
\]

### Step 2: Substitute known values into the Ideal Gas Law
Given:
- \(P = 8.45 \, \text{atm}\)
- \(V = 70.0 \, L\)
- \(R = 0.0821 \, \text{L} \cdot \text{atm} / \text{mol} \cdot \text{K}\)
- \(T = 293.15 \, K\)

Plug in the values:

\[
n = \frac{PV}{RT} = \frac{(8.45 \, \text{atm})(70.0 \, L)}{(0.0821 \, \text{L} \cdot \text{atm} / \text{mol} \cdot \text{K})(293.15 \, K)}
\]

### Step 3: Calculate the right side of the equation
First, calculate the numerator:

\[
PV = 8.45 \, \text{atm} \times 70.0 \, L = 591.5 \, \text{atm} \cdot \text{L}
\]

Next, calculate the denominator:

\[
RT = 0.0821 \, \text{L} \cdot \text{atm} / \text{mol} \cdot \text{K} \times 293.15 \, K \approx 24.2 \, \text{L} \cdot \text{atm} / \text{mol}
\]

### Step 4: Calculate the number of moles \(n\)

Now substitute the values into the equation:

\[
n = \frac{591.5 \, \text{atm} \cdot \text{L}}{24.2 \, \text{L} \cdot \text{atm} / \text{mol}} \approx 24.4 \, \text{mol}
\]

Thus, the closest answer from the provided options is **c: 24.6 mol**.