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I was reading Phil Plait's 'Death from the skies' where it describes the fate of the universe. It describes the period from 10^90 years to infinity as the "dark age" when all the of the black holes have disappeared.

In this state the universe consists many particles. If two like-charged particles encounter each other, they are repelled. However, if two unlike-charged particles come close to each other, they will move towards each other and disappear to become light energy.

This wasn't covered in the book, but unless I've misunderstood things (which is quite likely), there will be a point when all of the mass in the universe has been reduced to zero after all the particles have paired up and become photons?

If so, is there an estimate when this event will occurr?

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Photons don't have zero mass. They have zero rest mass. Since they're never at rest, they do have non-zero energy, which is equivalent to mass (E=mc2). (There are other ways to look at it, such as that a photon has zero mass and non-zero energy -- but since mass and energy are fundamentally equivalent, it's pretty much the same thing. (This is where an actual physicist jumps in and tells me I'm wrong.))

For example, the path of a beam of light is actually bent by gravity. We can see this in the gravitational lens phenomenon. And light, because it has mass/energy, exerts a gravitational pull of its own, though it's so small as to be undetectable in any but the most extreme conditions.

If things happen as you describe (all the mass of the universe decaying to photons), then the universe might reach zero rest mass, but the conservation of mass-energy still applies.

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Two unlike charged particles don't disappear to become light energy. Although it seems like protons and electrons have opposite charges and would cancel each other out if they met, this is not the case. A proton consists of two up quarks and one down quark. An up quark has +2/3 charge and a down quark has a -1/3 charge. A neutron is two down quarks and an up quark. The mass and electrical charge of a down quark is the same as the net mass and electrical charge of an up quark combined with an electron. A down quark can decay into an up quark and an electron. An electron striking an atomic nucleus will sometimes be absorbed by the nucleus and changing an up quark into a down quark, changing a proton into a neutron. This happens in the upper atmosphere when Nitrogen 14 becomes Carbon 14. The point of this is that an up quark and an electron do not cancel each other out because the electron is a negative 1 charge and the up quark is a positive 2/3 charge. Changing them both into a photon would violate the law of conservation of electric charge.

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Let us clear up some things.

The end of an expanding universe is a matter of models.

The concept of mass is connected with energy as

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for each individual particle. E and p are a four vector ruled by Lorenz transformations.

For a single particle that is the momentum energy four vector of the particle, and when it is at rest m is the rest mass of the particle. For more than one particle it is called the invariant mass, and when they are all at rest, it is the addition of their rest masses. When in motion, which is the usual state of particles in vacuum, there will always exist an invariant mass for an agglomerate of particles, and certainly for the universe.

Even zero mass particles can have (in a group) an invariant mass when more than one , as the existence of the pi0 meson demonstrates.

if two unlike-charged particles come close to each other, they will move towards each other and disappear to become light energy.

This will happen, an annihilation, only if all the quantum numbers are equal and opposite, and depending on the model the debris may be massive. Proton antiproton annihilate into a lot of mesons which in the end decay into leptons and photons, i.e. electrons positrons and neutrinos. It is at the end of the chain of decays that one may talk of end particles.

In the standard model of particle physics protons do not decay. In the standard model of cosmology there is observed baryon asymmetry , thus one expects protons to retain their identity to the end of time. BUT it is sure that there will be an extension of the standard model necessary due to small discrepancies , and in these extensions protons will decay and neutrinos have (small) masses and in this case everything will be photons at the very end of the decay and interaction chains, light of very large wavelength ( low energy photons due to the expansion of the universe).

This wasn't covered in the book, but unless I've misunderstood things (which is quite likely), there will be a point when all of the mass in the universe has been reduced to zero after all the particles have paired up and become photons?

You have misunderstood, all the rest masses of individual photons will be zero, but they will carry energy and momentum ( however small) and move with velocity c always, thus there will be an invariant mass from the addition of all the four vectors of the universe's photons, the end particles if protons decay.

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