Calculate the weight of H2 in a storage tank of 5,000 cubic meters at a pressure of 700 bar. (temperature 27 degrees Celsius)
Assume molar volume of hydrogen =22.4 liters (at 27 degrees Celsius)
1 mol of hydrogen =2 g
Hint: Calculate number of H2 mols inside the tank first

To calculate the weight of hydrogen (H₂) in a storage tank, we can follow these steps:

### Step 1: Convert Volume of the Tank to Liters
Since the molar volume of hydrogen is given in liters, we need to convert the volume of the tank from cubic meters to liters.

\[
1 \, \text{m}^3 = 1,000 \, \text{liters}
\]

Thus, the volume of the tank is:

\[
V_{\text{tank}} = 5,000 \, \text{m}^3 = 5,000 \times 1,000 = 5,000,000 \, \text{liters}
\]

### Step 2: Apply the Ideal Gas Law for Hydrogen
Since the pressure and temperature are different from standard conditions, we will use the ideal gas law to calculate the number of moles of hydrogen in the tank. The ideal gas law is given by:

\[
PV = nRT
\]

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

We need to convert the temperature from Celsius to Kelvin:
\[
T = 27 + 273 = 300 \, \text{K}
\]

Now, solving for \( n \) (the number of moles):

\[
n = \frac{PV}{RT}
\]

Substituting the known values:

\[
n = \frac{(700 \, \text{bar})(5,000,000 \, \text{liters})}{(0.0821 \, \text{L·bar/(mol·K)})(300 \, \text{K})}
\]

Let's calculate the number of moles.The number of moles of hydrogen (\(n\)) in the tank is approximately \(142,103,126.27\) moles.

### Step 3: Calculate the Mass of Hydrogen
Now, we can calculate the mass of hydrogen using the fact that 1 mole of hydrogen weighs 2 grams.

\[
\text{Mass of H}_2 = n \times 2 \, \text{g/mol}
\]

\[
\text{Mass of H}_2 = 142,103,126.27 \times 2 = 284,206,252.54 \, \text{g}
\]

Converting this to kilograms:

\[
\text{Mass of H}_2 = 284,206,252.54 \, \text{g} \div 1000 = 284,206.25 \, \text{kg}
\]

### Conclusion:
The weight of hydrogen in the storage tank is approximately **284,206.25 kilograms**.

Would you like further details or have any questions?

Here are 5 related questions:
1. How would the weight change if the pressure increased to 800 bar?
2. What would happen to the number of moles if the temperature increased?
3. How do we calculate the mass for other gases stored under similar conditions?
4. What is the molar volume of hydrogen at different temperatures?
5. How does the ideal gas law deviate for real gases at high pressures?

**Tip:** Always double-check units to ensure consistency, especially when using different measurement systems.

Calculate the weight of H2 in a storage tank of 5,000 cubic meters at a pressure of 700 bar. (temperature 27 degrees Celsius)
Assume molar volume of hydrogen = 22.4 liters (at 27 degrees Celsius)
1 mol of hydrogen = 2 g
Hint: Calculate number of H2 mols inside the tank first.

This problem involves calculating the weight of hydrogen (H2) in a 5,000 cubic meter storage tank at 700 bar and 27°C. Learn to apply the ideal gas law (PV = nRT) to determine the number of moles and mass of hydrogen. Detailed steps and unit conversions provided.

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