Physics Examples

$P V = n R T$

$P$	$=$	$?$
$V$	$=$	$8.22 L$
$n$	$=$	$1 mol$
$T$	$=$	$32 ° F$

Step 1

Solve for $P$ .

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Step 1.1

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

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Step 1.1.1

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

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

Step 1.1.2

Simplify the left side.

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Step 1.1.2.1

Cancel the common factor of $V$ .

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Step 1.1.2.1.1

Cancel the common factor.

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

Step 1.1.2.1.2

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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Step 2.1

Substitute $8.22 L$ for $V$ .

$P = \frac{n R T}{8.22 L}$

Step 2.2

Substitute $1 mol$ for $n$ .

$P = \frac{1 mol R T}{8.22 L}$

Step 2.3

Convert $32 ° F$ to Kelvin.

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Step 2.3.1

Convert to Celsius.

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Step 2.3.1.1

This is the conversion formula for Fahrenheit to Celsius, where $T_{F}$ is temperature in Fahrenheit and $T_{C}$ is temperature in Celsius.

$T_{C} = \frac{5}{9} (T_{F} - 32)$

Step 2.3.1.2

Substitute the Fahrenheit temperature into the formula.

$\frac{5}{9} (32 ° - 32) C$

Step 2.3.1.3

Divide $5$ by $9$ .

$0.\overline{5} (32 ° - 32) C$

Step 2.3.1.4

Subtract $32$ from $32 °$ .

$0.\overline{5} \cdot 0 C$

Step 2.3.1.5

Multiply $0.\overline{5}$ by $0$ .

$0 C$

Step 2.3.2

To convert Celsius to Kelvin, add $273.15$ .

$(0 + 273.15) K$

Step 2.3.3

Add $0$ and $273.15$ .

$273.15 K$

Step 2.4

Substitute $273.15 K$ for $T$ .

$P = \frac{1 mol R (273.15 K)}{8.22 L}$

Step 2.5

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

$P = \frac{1 mol (0.08206 \frac{L atm}{K mol}) (273.15 K)}{8.22 L}$

$P = \frac{1.00 mol (0.08206 \frac{L atm}{K mol}) (273.15 K)}{8.22 L}$

Step 3

Simplify the right side.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Multiply $0.08206$ by $1.00$ .

$P = \frac{0.08206 mol \frac{L atm}{K mol} \cdot 273.15 K}{8.22 L}$

Step 3.1.2

Multiply $273.15$ by $0.08206$ .

$P = \frac{22.4146890 mol \frac{L atm}{K mol} K}{8.22 L}$

Step 3.1.3

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

$P = \frac{22.4146890 mol (- \frac{- L atm}{K mol}) K}{8.22 L}$

Step 3.1.4

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

$P = \frac{22.4146890 mol (- 1 \frac{- L atm}{K mol}) K}{8.22 L}$

Step 3.1.5

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

$P = \frac{22.4146890 mol \cdot - 1 (- \frac{K L atm}{K mol})}{8.22 L}$

Step 3.1.6

Multiply $- 1$ by $22.4146890$ .

$P = \frac{- 22.4146890 mol (- \frac{K L atm}{K mol})}{8.22 L}$

Step 3.1.7

Multiply $- 1$ by $- 22.4146890$ .

$P = \frac{22.4146890 mol \frac{K L atm}{K mol}}{8.22 L}$

Step 3.2

Simplify the numerator.

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Step 3.2.1

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

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Step 3.2.1.1

Cancel $K$ .

$P = \frac{22.4146890 mol \frac{K L atm}{K mol}}{8.22 L}$

Step 3.2.1.2

Rewrite the expression.

$P = \frac{22.4146890 mol \frac{1 (L atm)}{mol}}{8.22 L}$

Step 3.2.2

Combine exponents.

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Step 3.2.2.1

Combine $\frac{1 (L atm)}{mol}$ and $22.4146890$ .

$P = \frac{1 \cdot 22.4146890 \frac{L atm}{mol} mol}{8.22 L}$

Step 3.2.2.2

Multiply $22.4146890$ by $1$ .

$P = \frac{22.4146890 \frac{L atm}{mol} mol}{8.22 L}$

Step 3.2.2.3

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

$P = \frac{22.4146890 (- \frac{- L atm}{mol}) mol}{8.22 L}$

Step 3.2.2.4

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

$P = \frac{22.4146890 (- 1 \frac{- L atm}{mol}) mol}{8.22 L}$

Step 3.2.2.5

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

$P = \frac{22.4146890 \cdot - 1 (- \frac{mol L atm}{mol})}{8.22 L}$

Step 3.2.2.6

Multiply $22.4146890$ by $- 1$ .

$P = \frac{- 22.4146890 (- \frac{mol L atm}{mol})}{8.22 L}$

Step 3.2.2.7

Multiply $- 1$ by $- 22.4146890$ .

$P = \frac{22.4146890 \frac{mol L atm}{mol}}{8.22 L}$

Step 3.2.3

Cancel $mol$ .

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Step 3.2.3.1

Cancel $mol$ .

$P = \frac{22.4146890 \frac{mol L atm}{mol}}{8.22 L}$

Step 3.2.3.2

Divide $L atm$ by $1$ .

$P = \frac{22.4146890 (L atm)}{8.22 L}$

$P = \frac{22.4146890 L atm}{8.22 L}$

Step 3.3

Cancel $L$ .

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Step 3.3.1

Cancel $L$ .

$P = \frac{22.4146890 L atm}{8.22 L}$

Step 3.3.2

Rewrite the expression.

$P = \frac{22.4146890 atm}{8.22}$

Step 3.4

Rewrite the expression.

$P = 2.72684781 \frac{1 atm}{1}$

Step 3.5

Combine fractions.

$P = 2.72684781 atm$

Step 4

Round to $3$ significant figures.

$P = 2.73 atm$

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