Consider the reaction represented by the equation $\ce{2X + 2Z -> X2Z2}$. During a reaction in which a large excess of reactant $\ce{X}$ was present, the concentration of reaction $\ce{Z}$ was monitored over time. A plot of the natural logarithm of the concentration of $\ce{Z}$ versus time is shown in the figure above. The order of the reaction with respect to reactant $\ce{Z}$ is

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If the plot of the natural logarithm of a reactant concentration versus time is linear, the reaction is first order.

If you can do a bit of calculus, you can integrate the rate equation for first order to check:

$$\text{rate} = k[\ce{Z}]^1 \tag*{first-order rate equation}$$ $$\frac{dZ}{dt} = -k[\ce{Z}]$$ $$\frac{1}{\ce{Z}} dZ = -k dt$$ $$\int\frac{1}{\ce{Z}} dZ = \int-k dt$$ $$\ln[\ce{Z}]=-kt+C$$

At time 0, $C=\ln[\ce{Z}]_0$

$$\ln[\ce{Z}]=-kt+\ln[\ce{Z}]_0$$

This is the line of $\ln[\ce{Z}]$ versus $t$ with slope $-k$.