cookiethedog13
Answered

Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Discover comprehensive solutions to your questions from a wide network of experts on our user-friendly platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

What is the mole fraction of a solution prepared by dissolving 50.0 g of potassium permanganate [tex]$KMnO_4$[/tex] in 75.0 g of water?

A) 0.076
B) 0.071
C) 7.06
D) 0.55

Sagot :

GinnyAnswer
To determine the mole fraction of a solution prepared by dissolving 50.0 grams of potassium permanganate ([tex]$KMnO_4$[/tex]) in 75.0 grams of water ([tex]$H_2O$[/tex]), follow these steps:

### Step 1: Calculate the Molar Mass of [tex]$KMnO_4$[/tex]

First, determine the molar mass of [tex]$KMnO_4$[/tex]. The atomic masses are:
- Potassium (K): 39.1 g/mol
- Manganese (Mn): 54.9 g/mol
- Oxygen (O): 16.0 g/mol

The molar mass of [tex]$KMnO_4$[/tex] is calculated as:
[tex]\[ 39.1 + 54.9 + (16 \times 4) = 39.1 + 54.9 + 64 = 158.0 \text{ g/mol} \][/tex]

### Step 2: Calculate the Number of Moles of [tex]$KMnO_4$[/tex]

Using the mass of [tex]$KMnO_4$[/tex] (50.0 grams) and its molar mass (158.0 g/mol), calculate the moles of [tex]$KMnO_4$[/tex]:
[tex]\[ \text{Moles of } KMnO_4 = \frac{50.0 \text{ g}}{158.0 \text{ g/mol}} = 0.316455696 \text{ moles} \][/tex]

### Step 3: Calculate the Molar Mass of Water ([tex]$H_2O$[/tex])

The molar mass of water ([tex]$H_2O$[/tex]) is calculated using the atomic masses of hydrogen (H) and oxygen (O):
- Hydrogen (H): 1.01 g/mol each
- Oxygen (O): 16.0 g/mol

The molar mass of [tex]$H_2O$[/tex] is:
[tex]\[ (2 \times 1.01) + 16 = 2.02 + 16 = 18.02 \text{ g/mol} \][/tex]

### Step 4: Calculate the Number of Moles of Water

Using the mass of water (75.0 grams) and its molar mass (18.02 g/mol), calculate the moles of water:
[tex]\[ \text{Moles of water} = \frac{75.0 \text{ g}}{18.02 \text{ g/mol}} = 4.162042175 \text{ moles} \][/tex]

### Step 5: Calculate the Total Number of Moles

Sum the moles of [tex]$KMnO_4$[/tex] and water to get the total moles:
[tex]\[ \text{Total moles} = \text{Moles of } KMnO_4 + \text{Moles of water} = 0.316455696 + 4.162042175 = 4.478497871 \text{ moles} \][/tex]

### Step 6: Calculate the Mole Fraction of [tex]$KMnO_4$[/tex]

The mole fraction of [tex]$KMnO_4$[/tex] is the ratio of the moles of [tex]$KMnO_4$[/tex] to the total moles:
[tex]\[ \text{Mole fraction of } KMnO_4 = \frac{\text{Moles of } KMnO_4}{\text{Total moles}} = \frac{0.316455696}{4.478497871} = 0.070661124 \][/tex]

### Conclusion

The mole fraction of the solution prepared by dissolving 50.0 g of potassium permanganate in 75.0 g of water is approximately 0.071. Therefore, the correct answer is:

[tex]\[ \boxed{0.071} \][/tex]

So, the correct choice is:
[tex]\[ \text{B) 0.071} \][/tex]
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.