The ideal gas law relates pressure , volume , temperature , the amount of substance , and the universal gas constant by the equation Which of the following equations gives in terms of , , , and ?

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SAT Equivalent Expressions Question 1 | Free SAT Prep | Aniko

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Question 1·Easy·Equivalent Expressions

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The ideal gas law relates pressure $P$ , volume $V$ , temperature $T$ , the amount of substance $n$ , and the universal gas constant $R$ by the equation

P V = n R T.

Which of the following equations gives $R$ in terms of $P$ , $V$ , $n$ , and $T$ ?

For formula-rearrangement questions like this on the SAT, treat the equation exactly as you would a simple algebra equation: identify the variable you need (here, $R$ ), see what operations are being applied to it, and then use inverse operations step by step to isolate it. Keep track of which factors are on the same side as the target variable—only those need to be “undone”—and remember to perform the same operation on both sides so the equality stays true. Once you have the variable alone, rewrite the result in a clean form and match it to the closest answer choice.

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Focus on what the question is asking for

You are given $PV = nRT$ but the question wants an equation that starts with $R =$ . Think of this like solving an equation for $R$ .

Look at how R appears in the equation

In $PV = nRT$ , $R$ is not alone; it is multiplied by $n$ and by $T$ . Ask yourself: what operation will get rid of those factors next to $R$ ?

Apply the inverse operation correctly

To isolate $R$ , you need to divide both sides of the equation by the same thing. What single expression made of $n$ and $T$ should you divide by so that only $R$ is left on that side?

Desmos Guide

Set up variables as sliders

In Desmos, add sliders for the four variables: type P=2, V=3, n=1, and T=4 on separate lines (Desmos will create sliders for each). You can change these values later to test more cases.

Write the original equation using a symbolic R

On a new line, type the expression for the left side and the right side separately, for example: left = P*V and right = n*R*T. You will plug each answer choice into R in turn to see which one makes left and right equal.

Test each choice for R

For each answer choice, define a version of R and compare the two sides:

For choice A, type RA = P*V*n*T and then checkA = left - n*RA*T.
For choice B, type RB = P*V/(n*T) and then checkB = left - n*RB*T.
For choice C, type RC = n*T/(P*V) and then checkC = left - n*RC*T.
For choice D, type RD = n*P/(V*T) and then checkD = left - n*RD*T.

Now move the sliders for $P$ , $V$ , $n$ , and $T$ . The correct formula for $R$ will be the one whose corresponding check expression stays equal to 0 for all slider values you try.

Step-by-step Explanation

Identify the target variable and its operations

You are given the ideal gas law:

PV = nRT

The question asks for an equation that gives $R$ in terms of $P$ , $V$ , $n$ , and $T$ . That means you need to rewrite this equation so that $R$ is alone on one side, with everything else on the other side. Notice that on the right-hand side, $R$ is multiplied by $n$ and by $T$ .

Decide how to isolate R

Because $R$ is being multiplied by $n$ and $T$ , you need to undo that multiplication. To undo multiplication, use division. So you should divide both sides of the equation by the product $nT$ . Doing this will leave $R$ by itself on one side of the equation.

Carry out the division and match to an answer choice

Divide both sides of the original equation by $nT$ :

\frac{PV}{nT} = R.

Now rewrite it with $R$ on the left:

R = \frac{PV}{nT}.

This exactly matches answer choice B) $R = PV / (nT)$ , so B is correct.

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Step-by-step Explanation

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