Calculate the number of moles in 158 grams of ` KMnO_4`

Answer

To calculate the number of moles in 158 grams of \( KMnO_4 \), follow these steps:

### Step 1: Understand the formula for calculating moles
The number of moles (\( n \)) can be calculated using the formula:
\[ n = \frac{\text{given mass (g)}}{\text{molar mass (g/mol)}} \]

### Step 2: Identify the given mass
The given mass of \( KMnO_4 \) is 158 grams.

### Step 3: Calculate the molar mass of \( KMnO_4 \)
To find the molar mass, we need to sum the atomic masses of each element in the compound:
- Potassium (K): 39 g/mol
- Manganese (Mn): 55 g/mol
- Oxygen (O): 16 g/mol (and there are 4 oxygen atoms)

Now, calculate the total molar mass:
\[ \text{Molar mass of } KMnO_4 = \text{mass of K} + \text{mass of Mn} + 4 \times \text{mass of O} \]
\[ = 39 + 55 + (4 \times 16) \]
\[ = 39 + 55 + 64 \]
\[ = 158 \text{ g/mol} \]

### Step 4: Substitute the values into the moles formula
Now that we have both the given mass and the molar mass, we can substitute these values into the moles formula:
\[ n = \frac{158 \text{ g}}{158 \text{ g/mol}} \]

### Step 5: Calculate the number of moles
\[ n = 1 \text{ mole} \]

### Final Answer
The number of moles in 158 grams of \( KMnO_4 \) is **1 mole**.

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