The arginine$-$tRNA synthetase enzyme catalyzes the

reaction that charges a tRNA with the amino acid

arginine:

ATP $+$ arginine $+$ tRNA $AMP+P+$ arginyl$-$tRNA

The value of the equilibrium constant is $1\mathrm{.}13.$

At equilibrium, following an in vitro reaction, the

concentration of ATP is $2M,$ of arginine is $500mM,$ and

of arginyl$-$tRNA is $10M.$ The concentrations of AMP

and of $P{P}_i$ are $500M.$ What is the concentration of

arginyl$-$tRNA? Please make sure you explain every step of the calculation and justify any assumptions you make. Please write clearly