$A$ balloon has $5.0$ $g$ mole of helium at $7^{\circ} C$. Calculate
$(a)$ the number of atoms of helium in the balloon,
$(b)$ the total internal energy of the system.

(N/A) The internal energy of a monoatomic gas is given by $U = \frac{3}{2} nRT$,where $n$ is the number of moles,$R$ is the universal gas constant,and $T$ is the temperature in Kelvin.
Given:
$n = 5.0$ moles
$T = 7^{\circ} C = 7 + 273 = 280 \ K$
$N_{A} = 6.022 \times 10^{23} \ \text{atoms/mol}$
$R = 8.314 \ J/(mol \cdot K)$
$(a)$ Number of helium atoms:
$N = n \times N_{A} = 5.0 \times 6.022 \times 10^{23} = 3.011 \times 10^{24} \ \text{atoms}$.
$(b)$ Total internal energy of the system:
$U = \frac{3}{2} nRT = \frac{3}{2} \times 5.0 \times 8.314 \times 280$
$U = 1.5 \times 5.0 \times 8.314 \times 280 = 17459.4 \ J \approx 1.75 \times 10^{4} \ J$.