VIPSolutionsAct like a helpful tutor and exlain me : Give step-by-step solution with explanation and final answer:6.) Fuel cell powered vehicles used hydrogen as fuel source. Examples include the Toyota Mirai, Honda Clarity, and Hyundai NEXO. To achieve an acceptable range, the hydrogen is compressed and stored onboard vehicles at up to 700 bar!!! Suppose your fuel cell car ran completely empty. You fil the car to the maximum pressure and assume the gas is at 25 °C. You fill the tank with 10 kg of Hz, what is the estimated volume of your tank? (5 pts)
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Give step-by-step solution with explanation and final answer:
6.) Fuel cell powered vehicles used hydrogen as fuel source. Examples include the Toyota
Mirai, Honda Clarity, and Hyundai NEXO. To achieve an acceptable range, the hydrogen is
compressed and stored onboard vehicles at up to 700 bar!!! Suppose your fuel cell car ran
completely empty. You fil the car to the maximum pressure and assume the gas is at 25 °C.
You fill the tank with 10 kg of Hz, what is the estimated volume of your tank? (5 pts)
This is AI generated Response.
Asked by: manish kumar
Created at: 2025-09-24 02:48:48
Asked by: manish kumar
Created at: 2025-09-24 02:48:48
Final Answer:
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Let's solve the problem step by step:
---
## **Step 1: Write Down Given Data**
- **Mass of H₂ (\( m \))** = 10 kg
- **Pressure (\( P \))** = 700 bar = 700 × 10⁵ Pa = 7.00 × 10⁷ Pa
- **Temperature (\( T \))** = 25°C = 273 + 25 = 298 K
- **Molar mass of H₂ (\( M \))** = 2.016 g/mol = 0.002016 kg/mol
- **Universal gas constant (\( R \))** = 8.314 J/(mol·K)
---
## **Step 2: Find Number of Moles (\( n \))**
\[
n = \frac{m}{M}
\]
\[
n = \frac{10 \text{ kg}}{0.002016 \text{ kg/mol}} = 4960.32 \text{ mol}
\]
---
## **Step 3: Use the Ideal Gas Law to Find Volume**
The ideal gas law is:
\[
PV = nRT
\]
Rearrange for \( V \):
\[
V = \frac{nRT}{P}
\]
---
## **Step 4: Plug in the Values**
\[
V = \frac{4960.32 \times 8.314 \times 298}{7.00 \times 10^7}
\]
Calculate the numerator:
\[
4960.32 \times 8.314 \times 298 \approx 12,282,693.5
\]
Now, divide by the denominator:
\[
V = \frac{12,282,693.5}{70,000,000} \approx 0.175 \text{ m}^3
\]
---
## **Step 5: Final Answer**
### **Estimated Volume of the Tank**
\[
\boxed{0.18 \ \text{m}^3}
\]
(Rounded to two decimal places; 0.175 m³ ≈ 175 liters.)
---
## **Summary Table**
| Quantity | Value |
|---------------|--------------|
| Mass | 10 kg |
| Pressure | 700 bar |
| Temperature | 25°C (298 K) |
| Volume | ~0.18 m³ |
---
### **Explanation**
- We used the ideal gas law, assuming hydrogen behaves ideally at these conditions (a simplification).
- Compressed hydrogen at 700 bar and room temperature fills a tank of about 175 liters for 10 kg H₂.
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