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My chemistry teacher used to tell us that if you had a soup bowl with only electrons in it, the explosion could make you fly to Pluto. Was he right? Could this happen?

The answer would depend how densely the electrons are packed. Let's say we have 1 kg of electrons, meaning we would have about $N = 10^30$ of them. For simplicity, let's approximate by arranging all of these electrons arranged in a spherical shell of radius $r=0.1$ meters. By symmetry, the voltage at the location of each charge would be constant and would have the following value.

$$V = -frac14pi epsilon_0fracNer$$

We can thus compute the potential energy $U = frac12Q V$ associated with this configuration.

$$U = frac12 cdot Ne cdot frac14pi epsilon_0fracNer = fracN^2 e^28 pi epsilon_0 r approx boxed1.15 times 10^33 text Joules$$

Ignoring air friction, the Earth's escape velocity is $v =11200$ meters / second, which for a $m=2times 10^6$ kg space shuttle, would only require $E = frac12 mv^2 = 1.25 times 10^14$ Joules.

So, yeah, you'd have way more than plenty sufficient energy.

A uniform sphere of radius $r$ and total charge $Q$ has an electric potential energy of $3Q^2/20pi epsilon_0 r$.

Let's say your bowl is like a sphere of radius 5 cm. If it's all water ( molecular weight 18$m_u$) and $mu= 9/5$ of a mass unit for every electron, then the number of electrons is
$ N_e = 1000 frac4pi r^33/mu m_u = 5times 10^26$

If all the nuclei were removed, the electric potential energy would be $7times 10^26$ Joules.

Pluto is at about 40 au from the Sun, effectively to get there, you have to escape from Earth and escape from the Sun. To do this you would need to launch from the Earth with a carefully directed speed of at least 16 km/s. If your mass is 100 kg, that takes a mere $1.3times 10^10$ J.