What is the Walras law vs first welfare theorem As far as I know, both of the first welfare theorem and the Walras law are closely tied to the invisible hand. what is the difference between them?

thank you very much for your help
Walras' law describes market equilibria conditions, which states roughly speaking that if there exists within an exchange economy market equilibria for $n-1$ good markets, then the last good market $n$ is also in equilibrium. Thus, we have a market system with $n$ equations and $n-1$ independent variables, where the last market is linear dependent from the other $n-1$ markets.   

Now, the first Welfare Theorem of Arrow states that for every exchange economy with convex preferences, every Walrasian equilibrium is Pareto efficient.   

The implication of the first Welfare Theorem is that we need no central planner to achieve a Pareto efficient outcome in an exchange economy. The Pareto efficient outcome is based on decentralized decisions within the exchange economy. If we now introduce transaction costs and incomplete information into the system, then it should be obvious that every decentralized economy is doing better than every centralized one due to the information problem.  

Update:

I forget to mention some interesting implications of Walras' law. The law reveals to us that we have only one degree of freedom. This implies that a central instance can only fix one price level, for instance, that of the numeraire good, the others prices of the markets are determined by the market forces. Hence, a central instance has no control on them. 

To make this argument more precise, let us apply this law to a central bank policy. We have only one degree of freedom, the central bank can now fix either the interest rate of the money market or a price index, but not both. If it fixes the interest rate, it has to accept the price levels and therefore the inflation rate, and vice versa for the price index. This also implies that a central bank cannot simultaneously targeting the price index and the unemployment rate of an economy.