To find the number of moles of hydrogen gas, we can use the Ideal Gas Law, which is expressed as:
\[ PV = nRT \]
Where:
- \( P \) = pressure (in bar)
- \( V \) = volume (in liters)
- \( n \) = number of moles
- \( R \) = ideal gas constant (in appropriate units)
- \( T \) = temperature (in Kelvin)
### Step 1: Convert the temperature from Celsius to Kelvin
The temperature is given as \( 27^\circ C \). To convert Celsius to Kelvin, we use the formula:
\[ T(K) = T(°C) + 273 \]
So,
\[ T = 27 + 273 = 300 \, K \]
### Step 2: Identify the values given in the problem
- Volume \( V = 18 \, L \)
- Pressure \( P = 0.92 \, \text{bar} \)
- Temperature \( T = 300 \, K \)
- Gas constant \( R = 0.083 \, \text{bar} \cdot \text{L}^{-1} \cdot \text{K}^{-1} \cdot \text{mol}^{-1} \)
### Step 3: Rearrange the Ideal Gas Law to solve for \( n \)
We need to find \( n \), so we rearrange the Ideal Gas Law:
\[ n = \frac{PV}{RT} \]
### Step 4: Substitute the values into the equation
Now, we substitute the known values into the equation:
\[ n = \frac{(0.92 \, \text{bar}) \times (18 \, L)}{(0.083 \, \text{bar} \cdot \text{L}^{-1} \cdot \text{K}^{-1} \cdot \text{mol}^{-1}) \times (300 \, K)} \]
### Step 5: Calculate the number of moles
Now we compute the values step by step:
1. Calculate the numerator:
\[ 0.92 \, \text{bar} \times 18 \, L = 16.56 \, \text{bar} \cdot L \]
2. Calculate the denominator:
\[ 0.083 \, \text{bar} \cdot \text{L}^{-1} \cdot \text{K}^{-1} \cdot \text{mol}^{-1} \times 300 \, K = 24.9 \, \text{bar} \cdot L \cdot \text{mol}^{-1} \]
3. Now divide the numerator by the denominator:
\[ n = \frac{16.56 \, \text{bar} \cdot L}{24.9 \, \text{bar} \cdot L \cdot \text{mol}^{-1}} \approx 0.6667 \, \text{mol} \]
### Step 6: Round the answer
Rounding \( 0.6667 \) gives us approximately \( 0.67 \, \text{mol} \).
### Final Answer:
The number of moles present in the gas is approximately \( 0.67 \, \text{mol} \).
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