Question

the equation pv = nrt is known as the ideal gas law equation and describes the behavior of gases under standard conditions. which of the following operations isolates the variable v?
(1/n)pv = nrt(1/n)
(1/p)pv = nrt(1/p)
(1/v)pv = nrt(1/v)
(1/t)pv = nrt(1/t)
question 8
1 pts
a shorthand method for isolating a variable is to move the other variables either down and over or up and over depending on whether they are numerators (above the line) or denominators (below the line).
which variable is isolated when v is moved down and over in pv = nrt and what is the corresponding equation?
t is isolated pv/nr = t
n is isolated pv/rt = n
p is isolated p = nrt/v
r is isolated pv/nt = r

Explanation:

Question 1

Step1: Isolate V in PV = nRT

Divide both sides by P.
$\frac{PV}{P}=\frac{nRT}{P}$
$V = \frac{nRT}{P}$ which is equivalent to multiplying both sides by $\frac{1}{P}$. So the correct operation is $(\frac{1}{P})PV=nRT(\frac{1}{P})$.

Step1: Move V "down and over" in PV = nRT

When we move V "down and over", we are dividing both sides of the equation by V. We get $P=\frac{nRT}{V}$. Then we can rewrite it as $\frac{nRT}{V}=P$. If we want to isolate another variable from this new - form, we can cross - multiply to get $nRT = PV$. But if we start from the operation of moving V "down and over" and look at the form of the options, when we move V "down and over" in PV = nRT, we get $\frac{PV}{nR}=T$.

Answer:

$(\frac{1}{P})PV=nRT(\frac{1}{P})$

Question 2