A boat goes down the riverA boat goes downstream along the river.
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First-order reaction, known half-life, find the remainder对于一级反应,半衰期公式为\(t_{1/2}=\frac{\ln2}{k}\)(其中\(t_{1/2}\)为半衰期,\(k\)为反应速率常数),由此可先求出反应速率常数\(k = \frac{\ln2}{t_{1/2}}\)。
一级反应的浓度 - 时间关系遵循公式\(\ln\frac{C}{C_0}=-kt\)(其中\(C_0\)为初始浓度,\(C\)为\(t\)时刻的浓度)。
如果已知半衰期\(t_{1/2}\),要求剩余浓度\(C\),可以先求出\(k\),再将\(k\)代入\(\ln\frac{C}{C_0}=-kt\),进而得到\(C = C_0e^{-kt}\),这样就可以根据初始浓度\(C_0\)、反应进行的时间\(t\)以及求出的反应速率常数\(k\)来计算出\(t\)时刻剩余的浓度\(C\)。
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