Physics Examples

$P V = n R T$

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

Step 1

Solve for

$P$ .

Tap for more steps...

Step 1.1

Divide each term in

$P V = n R T$ by

$V$ and simplify.

Tap for more steps...

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.

Tap for more steps...

Step 1.1.2.1

Cancel the common factor of

$V$ .

Tap for more steps...

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

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

Tap for more steps...

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.

Tap for more steps...

Step 2.3.1

Convert to Celsius.

Tap for more steps...

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.

Tap for more steps...

Step 3.1

Simplify the numerator.

Tap for more steps...

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.

Tap for more steps...

Step 3.2.1

Reduce the expression

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

Tap for more steps...

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.

Tap for more steps...

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

$mol$ .

Tap for more steps...

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

$L$ .

Tap for more steps...

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.

$P = 2.73 atm$

Enter YOUR Problem