The equivalent Potential difference across an inductor and a capacitor?
For the inductance your calculation is correct, as you have 
$$Z_L = jX_L$$
However, for the capacitance you should remember the sign of the impedance:
$$Z_C = -jX_C$$
Both capacitors and inductors are frequency dependent, so if you would just put a DC voltage source over the circuit you should expect different voltages. The inductor will look like a short with 0Ω impedance and the capacitor will be an infinitely high impedance.

The reactance and inductance values that are given are for a certain frequency and moment in time. 

The sign in the reactance formula originates from the frequency domain formula for the impedance of a capacitor:
$$Z_C = \frac{1}{j\omega C}$$
Rewriting this in the reactive part would result in 
$$Z_C = -j \frac{1}{\omega C}$$
where
$$\frac{1}{\omega C} = X_C$$