- #1
Dustinsfl
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Can this second order be changed into a system of first order:
$$
x''(t) = -\frac{\mu}{(\sqrt{x^2+y^2+z^2})^3}x
$$
$$
x''(t) = -\frac{\mu}{(\sqrt{x^2+y^2+z^2})^3}x
$$
Last edited:
Jester said:My guess - there are two more equations that go with this one!
Ackbach said:Let $x_{1}=x$ and $x_{2}=x'$. Then you have the first-order system
\begin{align*}
x_{1}'&=x_{2}\\
x_{2}'&=-\frac{\mu}{ \left(x_{1}^{2}+y^{2}+z^{2} \right)^{3/2}}.
\end{align*}
What are $y$ and $z$ doing? Are they independent functions of time?
2nd order reactions involve two reactant molecules coming together to form the product, while 1st order reactions involve only one reactant molecule breaking down into products.
The order of a reaction can be determined by analyzing the rate law equation. If the rate is directly proportional to the concentration of two reactants, the reaction is 2nd order. If the rate is directly proportional to the concentration of only one reactant, the reaction is 1st order.
Yes, it is possible for a reaction to have a fractional order. This occurs when the rate of the reaction is not directly proportional to the concentration of the reactants. It is commonly seen in complex reaction mechanisms where the rate is influenced by multiple factors.
In 0 order reactions, the rate of the reaction is not affected by the concentration of the reactants. This means that the reaction will proceed at a constant rate regardless of the amount of reactants present. In 2nd order reactions, the rate is directly proportional to the concentration of the reactants, meaning that the reaction rate will increase as the concentration of the reactants increases.
Yes, it is possible for a 2nd order reaction to become a 1st order reaction. This can occur when one of the reactants is present in a much higher concentration compared to the other reactant. In this case, the reaction rate will become dependent on the concentration of the reactant in lower abundance, making it a 1st order reaction.