2.4. The base of a quadrilateral pyramid is a rectangle with a diagonal equal to $b$, and the angle between the diagonals is $60^{\circ}$. Each of the lateral edges forms an angle of $45^{\circ}$ with the base plane. Find the volume of the pyramid.
2.4. According to the condition, $B D=b, \angle A O B=60^{\circ}$ (Fig.2.4); from this, it is easy to find that $A B=\frac{b}{2}, A D=\frac{b \sqrt{3}}{2}$. Therefore, $S_{\text {base }}=A B \cdot A D=\frac{b^{2} \sqrt{3}}{4}$. Since $\angle S A O=\angle S B O=\angle S C O=\angle S D O=45^{\circ}$, $S O$ is the height of the pyramid and $S O=\frac{b}{2}$. Thus,

$$
V=\frac{1}{3} S_{\text{base}} \cdot S O=\frac{b^{3} \sqrt{3}}{24} .
$$

Answer: $\frac{b^{3} \sqrt{3}}{24}$.