Write the balanced chemical equation for the production of \(\mathrm{P}_{2} \mathrm{O}_{5}\) from \(\mathrm{P}\) and \(\mathrm{O}_{2}\).

First, write down the unbalanced equation using the available information on the starting reactants phosphorus (P) and oxygen (O₂) and the desired product, phosphorus pentoxide (P₂O₅). \[ P + O_{2} \rightarrow P_{2}O_{5} \]

Next, count the number of atoms of each element on both the reactants and the products sides of the equation, and compare them to each other. Reactants: P = 1, O = 2 Products: P = 2, O = 5

Now, check if the number of atoms for each element in reactants and products sides of the equation is equal. If not, balance the equation by adjusting the coefficients in front of the involved species. We need to make sure the number of phosphorus and oxygen on both sides is equal. To balance the phosphorus atoms, we need to multiply the coefficient of P on the left side of the equation by 2: \[ 2P + O_{2} \rightarrow P_{2}O_{5} \] Now, we have 2 phosphorus atoms on both sides of the equation, but the oxygen atoms are still unbalanced. To balance the oxygen atoms, we need to multiply the coefficient of O₂ on the left side of the equation by 5/2: \[ 2P + \frac{5}{2}O_{2} \rightarrow P_{2}O_{5} \] Finally, to obtain whole number coefficients, multiply the entire equation by 2: \[ 4P + 5O_{2} \rightarrow 2P_{2}O_{5} \] Now, both the phosphorus and oxygen atoms are balanced on both sides of the equation.

Now, we have our balanced chemical equation for the production of phosphorus pentoxide from phosphorus and oxygen: \[ 4P + 5O_{2} \rightarrow 2P_{2}O_{5} \]