Suppose I have a ideal gas mixture consisting of two different types of ideal gases, say $A$ and $B$, in a container with volume $V_{tot}$. There are $N_A$ particles of gas $A$ and $N_B$ particles of gas $B$. The temperature and pressure of the mixture are denotes by $T$ and $P$. Can I still use the ideal gas law for each of the component? Take $A$ as an example, is the following true?
$$P_A=\rho_A \frac{R}{M_A}T,$$ and $$V_{\text{m},A}=\frac{V_{tot}}{N_A}=\frac{RT}{P_A}=\frac{M_A}{\rho_A}$$
where $P_\text{A}$ is the partial pressure, $M_A$ is the molar mass, $V_{\text{m},A}$ is the partial molar volume, and $\rho_A$ is the partial density of $A$, i.e., the mass of species $A$ per unit volume of the mixture gas. $R$ is the universal gas constant. Thanks a lot!