`16g` of oxygen at `37^(@)C` is mixed with `14g` of nitrogen at `27^(@)C`. Find the temperature of the mixture?

Explanation

To find the temperature of the mixture of oxygen and nitrogen, we can follow these steps:

### Step 1: Calculate the number of moles of oxygen (O2)
The formula for calculating the number of moles is:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \]
For oxygen:
- Mass of O2 = 16 g
- Molar mass of O2 = 32 g/mol

Calculating the moles:
\[ n_1 = \frac{16 \, \text{g}}{32 \, \text{g/mol}} = 0.5 \, \text{moles} \]

### Step 2: Calculate the number of moles of nitrogen (N2)
Using the same formula:
For nitrogen:
- Mass of N2 = 14 g
- Molar mass of N2 = 28 g/mol

Calculating the moles:
\[ n_2 = \frac{14 \, \text{g}}{28 \, \text{g/mol}} = 0.5 \, \text{moles} \]

### Step 3: Convert temperatures from Celsius to Kelvin
To convert Celsius to Kelvin, we use the formula:
\[ T(K) = T(°C) + 273 \]
For oxygen:
- Temperature \( T_1 = 37°C = 37 + 273 = 310 \, K \)

For nitrogen:
- Temperature \( T_2 = 27°C = 27 + 273 = 300 \, K \)

### Step 4: Use the formula for the final temperature of the mixture
The formula for the final temperature \( T \) of the mixture is given by:
\[ T = \frac{n_1 T_1 + n_2 T_2}{n_1 + n_2} \]
Substituting the values:
\[ T = \frac{(0.5 \times 310) + (0.5 \times 300)}{0.5 + 0.5} \]

### Step 5: Calculate the final temperature
Calculating the numerator:
\[ T = \frac{155 + 150}{1} = 305 \, K \]

### Step 6: Convert the final temperature back to Celsius
To convert from Kelvin to Celsius:
\[ T(°C) = T(K) - 273 \]
So,
\[ T(°C) = 305 - 273 = 32°C \]

### Final Answer
The temperature of the mixture is \( 32°C \).

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