To determine the conversion factor for converting from moles of Cr to moles of [tex]\( Cl_2 \)[/tex], we first need to examine the balanced chemical equation:
[tex]\[
2 Cr + 3 Cl_2 \rightarrow 2 CrCl_3
\][/tex]
From the balanced equation, we can observe the coefficients of each reactant. The coefficient of [tex]\( Cr \)[/tex] is 2 and the coefficient of [tex]\( Cl_2 \)[/tex] is 3. These coefficients indicate the ratio in which the reactants react with each other. Specifically, 2 moles of [tex]\( Cr \)[/tex] react with 3 moles of [tex]\( Cl_2 \)[/tex].
To find the conversion factor to convert from moles of [tex]\( Cr \)[/tex] to moles of [tex]\( Cl_2 \)[/tex], we use the mole ratio derived from the coefficients in the balanced equation. The mole ratio for [tex]\( Cr \)[/tex] to [tex]\( Cl_2 \)[/tex] is:
[tex]\[
\frac{3 \text{ moles of } Cl_2}{2 \text{ moles of } Cr}
\][/tex]
Therefore, the conversion factor is:
[tex]\[
\frac{3}{2} = 1.5
\][/tex]
So, the conversion factor to convert from moles of Cr to moles of [tex]\( Cl_2 \)[/tex] is 1.5.
