7. le volume dun gaz dans un ballon est de 1200 ml à une pression et à une température absolue données…

Explanation:

Step1: Recall the ideal - gas law

The ideal - gas law is $PV = nRT$, where $P$ is pressure, $V$ is volume, $n$ is the number of moles, $T$ is absolute temperature, and $R$ is the ideal - gas constant. Let the initial state be $P_1V_1=n_1RT_1$ and the final state be $P_2V_2=n_2RT_2$.

Step2: Identify the changes in the variables

We are given that $V_1 = 1200\ mL$, $V_2=\frac{V_1}{2}=600\ mL$, $T_2 = 3T_1$, and $n_2=\frac{n_1}{2}$.

Step3: Express $P_2$ in terms of $P_1$

From $P_1V_1=n_1RT_1$ and $P_2V_2=n_2RT_2$, we can write $\frac{P_1V_1}{n_1T_1}=\frac{P_2V_2}{n_2T_2}=R$. Then $P_2=\frac{n_2T_2V_1}{n_1T_1V_2}P_1$. Substitute $V_2=\frac{V_1}{2}$, $T_2 = 3T_1$, and $n_2=\frac{n_1}{2}$ into the above formula: [ \begin{align*} P_2&=\frac{\frac{n_1}{2}\times3T_1\times V_1}{n_1T_1\times\frac{V_1}{2}}P_1\ &= 3P_1 \end{align*} ]

Answer:

The final pressure is 3 times the initial pressure.