Rust is still a decade or more away from anything serious like C. Majority of the functional Rust libraries today depend on underlying C libraries.
Rust may try to replace C++ but replacing C is far away dream.
Let's wait when Mozilla (origin and major supporter for Rust language) can release Firefox in Rust, until than it's still a popular experiment in systems programming area.
Rust does not run any critical component like Linux Kernel today, when it will be able to do it than it can be considered as real systems programming language challenger to C. Right now most of it's safety guarantees are not really battle tested like C.