For each of the following equations, write the chemical formulas and balance the equation. Try to indicate all the physical states (solid, liquid, gas) as well.
(a) potassium + water $\rightarrow$ potassium hydroxide $+_{-}$ hydrogen
(b) potassium hydride $+$ water $\rightarrow$ potassium hydroxide + hydrogen
(c) silicon dioxide $+$ carbon $\rightarrow$ silicon carbide $+$ carbon monoxide
(d) silicon dioxide + hydrogen fluoride $\rightarrow$ silicon tetrafluoride $+$ water
(e) phosphorus + chlorine $\rightarrow$ phosphorus trichloride