How many liters of gaseous hydrogen bromide at 27.0 degrees Celsius and 0.840 atm will a chemist need in order to prepare 3.50L of  1.20M hydrobromic acid? Be sure your answer has the correct number of significant figures.

Note: Reference the Fundamental constants table for additional information.

To solve this problem, we need to determine the volume of gaseous hydrogen bromide (HBr) required to prepare 3.50 L of 1.20 M hydrobromic acid (HBr(aq)).

### Steps:

1. **Moles of HBr required**:
   \[
   M = \dfrac{\text{moles of solute}}{\text{volume of solution in liters}}
   \]
   Rearranging for moles of HBr:
   \[
   \text{moles of HBr} = M \times V
   \]
   where:
   - \( M = 1.20 \, \text{M} \)
   - \( V = 3.50 \, \text{L} \)
   
   \[
   \text{moles of HBr} = 1.20 \times 3.50 = 4.20 \, \text{moles}
   \]
   
2. **Volume of gaseous HBr using the Ideal Gas Law**:
   We use the ideal gas law to calculate the volume of hydrogen bromide gas at the given conditions:
   
   \[
   PV = nRT
   \]
   Solving for \( V \):
   \[
   V = \dfrac{nRT}{P}
   \]
   where:
   - \( P = 0.840 \, \text{atm} \)
   - \( n = 4.20 \, \text{mol} \)
   - \( R = 0.0821 \, \text{L} \cdot \text{atm} / \text{mol} \cdot \text{K} \)
   - \( T = 27.0^\circ \text{C} + 273.15 = 300.15 \, \text{K} \)

   Now substituting the values:
   \[
   V = \dfrac{4.20 \times 0.0821 \times 300.15}{0.840}
   \]

   \[
   V = \dfrac{103.34643}{0.840} = 123.03 \, \text{L}
   \]

### Final Answer:
The chemist will need **123 L** of gaseous hydrogen bromide (rounded to 3 significant figures, based on the given data).

Would you like a detailed explanation of any part? Let me know!

Here are 5 follow-up questions for practice:
1. What is the ideal gas law and when is it applicable?
2. How do you convert Celsius to Kelvin?
3. What is the value of the gas constant \(R\) and why is it important?
4. How do you determine the number of significant figures in your final answer?
5. How can the molarity of a solution be altered by changing the amount of solute or solvent?

**Tip**: Always ensure units are consistent (e.g., volume in liters, temperature in Kelvin) when using the ideal gas law.

How many liters of gaseous hydrogen bromide at 27.0 degrees Celsius and 0.840 atm will a chemist need in order to prepare 3.50L of 1.20M hydrobromic acid? Be sure your answer has the correct number of significant figures.

Determine the volume of hydrogen bromide gas required at 27.0°C and 0.840 atm to prepare 3.50L of 1.20M hydrobromic acid using stoichiometry and the ideal gas law. This problem involves calculating molarity, applying the ideal gas law, and ensuring the correct number of significant figures. Suitable for high school chemistry students in Grades 10-12.

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