To calculate the average translational kinetic energy of a molecule in an ideal gas, you can use the formula:
\[ \text{Average kinetic energy} (KE) = \frac{3}{2} k T \]
where:
- \( k \) is the Boltzmann constant, approximately \( 1.38 \times 10^{-23} , \text{J/K} \)
- \( T \) is the absolute temperature in Kelvin.
First, convert the temperature from degrees Celsius to Kelvin:
\[ T(K) = 29°C + 273.15 = 302.15 , K \]
Now, substitute \( T \) into the kinetic energy formula:
\[ KE = \frac{3}{2} (1.38 \times 10^{-23} , \text{J/K}) (302.15 , K) \]
Calculating this gives:
\[ KE = \frac{3}{2} \times 1.38 \times 10^{-23} \times 302.15 \]
\[ KE = \frac{3}{2} \times 4.16457 \times 10^{-21} , \text{J} \]
\[ KE \approx 6.24686 \times 10^{-21} , \text{J} \]
Thus, the average translational kinetic energy of a molecule of an ideal gas at a temperature of 29°C is approximately \( 6.25 \times 10^{-21} \) J.