To find the rate of change of [tex]\( NO \)[/tex] given the rate of change of [tex]\( Cl_2 \)[/tex], we need to consider the stoichiometry of the balanced chemical reaction:
[tex]\[ 2 NO (g) + Cl_2 (g) \longrightarrow 2 NOCl (g) \][/tex]
The reaction tells us that for every 1 mole of [tex]\( Cl_2 \)[/tex] that reacts, 2 moles of [tex]\( NO \)[/tex] also react. This stoichiometric relationship allows us to relate the rates of change of the respective reactants.
Step-by-step solution:
1. Identify the given rate of change:
The rate of change of [tex]\( Cl_2 \)[/tex] is given as [tex]\( -0.0510 \, M/s \)[/tex].
2. Understand the stoichiometric relationship:
According to the balanced chemical equation, 1 mole of [tex]\( Cl_2 \)[/tex] reacts with 2 moles of [tex]\( NO \)[/tex]. This means the rate of consumption of [tex]\( NO \)[/tex] is twice the rate of consumption of [tex]\( Cl_2 \)[/tex].
3. Setting up the relationship:
The rate of change of [tex]\( NO \)[/tex] can be calculated by multiplying the rate of change of [tex]\( Cl_2 \)[/tex] by the stoichiometric coefficient ratio of [tex]\( NO \)[/tex] to [tex]\( Cl_2 \)[/tex]:
[tex]\[
\text{Rate of change of } NO = 2 \times (\text{Rate of change of } Cl_2)
\][/tex]
4. Substitute the given rate:
Substitute the given rate of change of [tex]\( Cl_2 \)[/tex]:
[tex]\[
\text{Rate of change of } NO = 2 \times (-0.0510 \, M/s)
\][/tex]
5. Calculate the rate:
Performing the multiplication:
[tex]\[
\text{Rate of change of } NO = -0.102 \, M/s
\][/tex]
Therefore, the rate of change of [tex]\( NO \)[/tex] is [tex]\( -0.102 \, M/s \)[/tex].
