Is there a well-behaved finitely additive “measure” on $\mathbb{Q }$?

Question

There exists no nontrivial measure on the set of rational numbers for which the measure of singletons is zero. That’s because the rational numbers are countable, so any set of rational numbers is a countable union of singeltons, and so the measure of any set of rational numbers must be zero by countable additivity.

I’m interested in what happens if you weaken countable additivity to finite additivity. My question is does there exists a set function $m$ from some collection of subsets of $Q$ to the interval $[0,\infty]$ (in the extended real number system), with the following properties?

1. $m(\emptyset) = 0$
2. $m(\mathbb{Q})=\infty$
3. $m(X)=0$ if $X$ is a singleton.
4. $m((a,b)\cap\mathbb{Q})=b-a$ for any $a,b\in\mathbb{R}$
5. $m$ is finitely additive
6. If $A\subseteq B$ then $m(A)\leq m(B)$
7. $m$ is translation-invariant

Or is there no such $m$ with all these properties?