Physics Examples

$P V = n R T$

$P$	$=$	$?$
$V$	$=$	$98.52 L$
$n$	$=$	$2 mol$
$T$	$=$	$312 K$

Step 1

Solve for $P$ .

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Divide each term in $P V = n R T$ by $V$ and simplify.

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Divide each term in $P V = n R T$ by $V$ .

$\frac{P V}{V} = \frac{n R T}{V}$

Simplify the left side.

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Cancel the common factor of $V$ .

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Cancel the common factor.

$\frac{P V}{V} = \frac{n R T}{V}$

Divide $P$ by $1$ .

$P = \frac{n R T}{V}$

Step 2

Substitute the given values into $P = \frac{n R T}{V}$ .

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Substitute $98.52 L$ for $V$ .

$P = \frac{n R T}{98.52 L}$

Substitute $2 mol$ for $n$ .

$P = \frac{2 mol R T}{98.52 L}$

Substitute $312 K$ for $T$ .

$P = \frac{2 mol R (312 K)}{98.52 L}$

Substitute $0.08206 \frac{L atm}{K mol}$ for the constant $R$ .

$P = \frac{2 mol (0.08206 \frac{L atm}{K mol}) (312 K)}{98.52 L}$

$P = \frac{2.00 mol (0.08206 \frac{L atm}{K mol}) (312 K)}{98.52 L}$

Step 3

Simplify the right side.

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Simplify the numerator.

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Multiply $0.08206$ by $2.00$ .

$P = \frac{0.1641200 mol \frac{L atm}{K mol} \cdot 312 K}{98.52 L}$

Multiply $312$ by $0.1641200$ .

$P = \frac{51.2054400 mol \frac{L atm}{K mol} K}{98.52 L}$

Factor $- 1$ out of $\frac{L atm}{K mol}$ .

$P = \frac{51.2054400 mol (- \frac{- L atm}{K mol}) K}{98.52 L}$

Rewrite $- \frac{- L atm}{K mol}$ as $- 1 \frac{- L atm}{K mol}$ .

$P = \frac{51.2054400 mol (- 1 \frac{- L atm}{K mol}) K}{98.52 L}$

Combine $K$ and $\frac{- L atm}{K mol}$ .

$P = \frac{51.2054400 mol \cdot - 1 (- \frac{K L atm}{K mol})}{98.52 L}$

Multiply $- 1$ by $51.2054400$ .

$P = \frac{- 51.2054400 mol (- \frac{K L atm}{K mol})}{98.52 L}$

Multiply $- 1$ by $- 51.2054400$ .

$P = \frac{51.2054400 mol \frac{K L atm}{K mol}}{98.52 L}$

Simplify the numerator.

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Reduce the expression $\frac{K L atm}{K mol}$ by cancelling the common factors.

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Cancel $K$ .

$P = \frac{51.2054400 mol \frac{K L atm}{K mol}}{98.52 L}$

Rewrite the expression.

$P = \frac{51.2054400 mol \frac{1 (L atm)}{mol}}{98.52 L}$

Combine exponents.

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Combine $\frac{1 (L atm)}{mol}$ and $51.2054400$ .

$P = \frac{1 \cdot 51.2054400 \frac{L atm}{mol} mol}{98.52 L}$

Multiply $51.2054400$ by $1$ .

$P = \frac{51.2054400 \frac{L atm}{mol} mol}{98.52 L}$

Factor $- 1$ out of $\frac{L atm}{mol}$ .

$P = \frac{51.2054400 (- \frac{- L atm}{mol}) mol}{98.52 L}$

Rewrite $- \frac{- L atm}{mol}$ as $- 1 \frac{- L atm}{mol}$ .

$P = \frac{51.2054400 (- 1 \frac{- L atm}{mol}) mol}{98.52 L}$

Combine $mol$ and $\frac{- L atm}{mol}$ .

$P = \frac{51.2054400 \cdot - 1 (- \frac{mol L atm}{mol})}{98.52 L}$

Multiply $51.2054400$ by $- 1$ .

$P = \frac{- 51.2054400 (- \frac{mol L atm}{mol})}{98.52 L}$

Multiply $- 1$ by $- 51.2054400$ .

$P = \frac{51.2054400 \frac{mol L atm}{mol}}{98.52 L}$

Cancel $mol$ .

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Cancel $mol$ .

$P = \frac{51.2054400 \frac{mol L atm}{mol}}{98.52 L}$

Divide $L atm$ by $1$ .

$P = \frac{51.2054400 (L atm)}{98.52 L}$

$P = \frac{51.2054400 L atm}{98.52 L}$

Cancel $L$ .

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Cancel $L$ .

$P = \frac{51.2054400 L atm}{98.52 L}$

Rewrite the expression.

$P = \frac{51.2054400 atm}{98.52}$

Rewrite the expression.

$P = 0.51974665 \frac{1 atm}{1}$

Combine fractions.

$P = 0.51974665 atm$

Step 4

Round to $3$ significant figures.

$P = 0.520 atm$

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