On an imaginary planet Argon makes up 0.87% by volume of air (air has a similar composition as on our home planet).  Calculate its solubility (M) in water at 20°C and 75.9 atm.  The Henry's law constant for Ar under these conditions is 15.5 mol/ L

atm.

Enter a number in M (moles/L) to 2 decimal places.

To calculate the solubility of argon in water at 20°C and 75.9 atm on this imaginary planet, we can use Henry's Law. Henry's Law states that the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid. The formula is:

\[
C = k_H \cdot P
\]

Where:
- \( C \) is the concentration of the gas in the liquid (solubility in mol/L).
- \( k_H \) is Henry's Law constant (in mol/L·atm).
- \( P \) is the partial pressure of the gas (in atm).

### Given Data:
- **Henry's Law constant (\( k_H \)) for argon** = 15.5 mol/L·atm
- **Total pressure (\( P_{\text{total}} \))** = 75.9 atm
- **Volume percentage of argon in air** = 0.87%

### Step-by-Step Calculation:

1. **Calculate the Partial Pressure of Argon (\( P_{\text{Ar}} \)):**

   \[
   P_{\text{Ar}} = P_{\text{total}} \times \frac{\text{Volume\% of Argon}}{100}
   \]

   \[
   P_{\text{Ar}} = 75.9 \, \text{atm} \times \frac{0.87}{100} = 0.66033 \, \text{atm}
   \]

2. **Calculate the Solubility of Argon (\( C \)) Using Henry's Law:**

   \[
   C = k_H \cdot P_{\text{Ar}}
   \]

   \[
   C = 15.5 \, \text{mol/L·atm} \times 0.66033 \, \text{atm} = 10.235115 \, \text{mol/L}
   \]

3. **Round to Two Decimal Places:**

   \[
   C = 10.24 \, \text{M}
   \]

### Final Answer:
The solubility of argon in water at 20°C and 75.9 atm is **10.24 M**.

---

**Do you have any questions or need further details? Here are some related questions to expand on this topic:**

1. How does temperature affect the solubility of gases in liquids according to Henry's Law?
2. What are the assumptions made in Henry's Law for gas solubility calculations?
3. How does the presence of other gases influence the solubility of a specific gas in a mixture?
4. Can Henry's Law be applied to non-ideal gases, and if so, how is it adjusted?
5. How does the solubility of a gas in water change with an increase in pressure?
6. What are some real-world applications of Henry's Law in environmental science?
7. How do you determine the Henry's Law constant for a gas under different conditions?
8. What is the relationship between partial pressure and mole fraction in a gas mixture?

**Tip:** When dealing with mixtures of gases, always determine the partial pressure of the specific gas of interest before applying Henry's Law.

Learn how to calculate the solubility of argon in water at 20°C and 75.9 atm using Henry's Law with a step-by-step solution. Given the Henry's Law constant for argon under these conditions and the partial pressure of argon in air, determine the solubility in moles per liter (M).

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