The kinetic energy of translation of the molecules in 50 g of $$CO_{2}$$ gas at $$17^{\circ}C$$ is

Mass of $$CO_{2}$$ given is 50 g. Molar mass of $$CO_{2}$$ is $$12 + 2 \times 16 = 44\;\mathrm{g\,mol^{-1}}$$.

Number of moles, $$n = \frac{\text{mass}}{\text{molar mass}} = \frac{50}{44} = 1.13636\;\mathrm{mol}\,.$$

Temperature, $$T = 17^\circ\mathrm{C} = 17 + 273 = 290\;\mathrm{K}\,.$$

Formula: For an ideal gas, total translational kinetic energy is given by $$E_{\mathrm{trans}} = \frac{3}{2}\,n\,R\,T\,.$$

Substituting values into $$E_{\mathrm{trans}}$$: $$E_{\mathrm{trans}} = \frac{3}{2} \times 1.13636 \times 8.314\;\mathrm{J\,mol^{-1}K^{-1}} \times 290\;\mathrm{K}\quad-(1)$$

Compute step by step:
$$1.13636 \times 8.314 = 9.449\quad(\text{approx})$$
$$9.449 \times 290 = 2740.21\quad(\text{approx})$$
$$\frac{3}{2} \times 2740.21 = 4110.315\quad(\text{approx})$$

The result is $$\approx 4.11\times10^3\;\mathrm{J}$$. The closest given option is Option B: $$4102.8\;\mathrm{J}\,.$$

Answer: Option B, $$4102.8\;\mathrm{J}\,.$$