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er a function $V_m=\frac{RT}{P},$ where $R$ is a constant and $P,V_m,$ and $T$ are independent variables. This relationship is called the ideal gas law.

a$.$ What is the value of $P$ for $N_2$ if $V=10.L,n=1$mol, and $T=300,K?$

b$.$ Evaluate the two, first partial derivatives of $P$ for the ideal gas law.

Consider a function $[P+\frac{a}{V_m^2}][V_m-b]=RT,$ where $R,a,$ and $b$ are constants and $P,V_m,$ and $T$ are independent variables. This relationship is called the van der Waals equation and a and $b$ are material specific constants, often called the van der Waals constants.

a$.$ Solve this function for $P.$

b$.$ What is the value of $P$ as described by the van der Wals equation for $N_2$ if $V=10.L,n=1$mol, and $T=300.K?$ Note: You will need to look up values for a and $b$ for $N_2.$ Remember to cite any references you use.

c$.$ Evaluate the two, first partial derivatives of $P$ for the van der Waals equation.

Comparing the ideal gas law and the van der Waals equation.

a$.$ What is the percent difference between the two pressures?

b$.$ Why are the values different?

c$.$ Would the agreement between the ideal gas law and van der Waals equation be better or worse if $V$ and $n$ were held fixed, but $T$ were increased to $400.K?$

d$.$ Would the agreement between the ideal gas law and van der Waals equation be better or worse if $T$ and $n$ were held fixed, but $V$ were decreased to $5.$ L$?$

Pls help with $1$b$,2$a$,$b and $3$a$,$b im lost and its due tonight