Chemistry Examples

$P_{1} = 12 atm$ $V_{1} = 0.23 L$ $T_{1} = 200 K$ $P_{2} = 14 atm$ , $T_{2} = 300 K$

Step 1

Use the combined gas law to find the missing variable in the equation. If the pressure, volume, and temperature are known for one state, and two of the three are known in the second state the law can be used to find the unknown.

$\frac{P_{1} V_{1}}{T_{1}} = \frac{P_{2} V_{2}}{T_{2}}$

Step 2

Fill in the known values.

$\frac{0.23 L}{200 K} = \frac{V}{300 K}$

Step 3

Solve for the unknown.

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Step 3.1

Rewrite the equation as $\frac{V}{300 K} = \frac{0.23 L}{200 K}$ .

$\frac{V}{300 K} = \frac{0.23 L}{200 K}$

Step 3.2

Multiply both sides by $300 K$ .

$\frac{V}{300 K} (300 K) = \frac{0.23 L}{200 K} (300 K)$

Step 3.3

Simplify.

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Step 3.3.1

Simplify the left side.

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Step 3.3.1.1

Simplify $\frac{V}{300 K} (300 K)$ .

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Step 3.3.1.1.1

Rewrite using the commutative property of multiplication.

$300 \frac{V}{300 K} K = \frac{0.23 L}{200 K} (300 K)$

Step 3.3.1.1.2

Cancel the common factor of $300$ .

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Step 3.3.1.1.2.1

Factor $300$ out of $300 K$ .

$300 \frac{V}{300 K} K = \frac{0.23 L}{200 K} (300 K)$

Step 3.3.1.1.2.2

Cancel the common factor.

$300 \frac{V}{300 K} K = \frac{0.23 L}{200 K} (300 K)$

Step 3.3.1.1.2.3

Rewrite the expression.

$\frac{V}{K} K = \frac{0.23 L}{200 K} (300 K)$

Step 3.3.1.1.3

Cancel the common factor of $K$ .

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Step 3.3.1.1.3.1

Cancel the common factor.

$\frac{V}{K} K = \frac{0.23 L}{200 K} (300 K)$

Step 3.3.1.1.3.2

Rewrite the expression.

$V = \frac{0.23 L}{200 K} (300 K)$

Step 3.3.2

Simplify the right side.

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Step 3.3.2.1

Simplify $\frac{0.23 L}{200 K} (300 K)$ .

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Step 3.3.2.1.1

Rewrite using the commutative property of multiplication.

$V = 300 \frac{0.23 L}{200 K} K$

Step 3.3.2.1.2

Cancel the common factor of $100$ .

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Step 3.3.2.1.2.1

Factor $100$ out of $300$ .

$V = 100 (3) \frac{0.23 L}{200 K} K$

Step 3.3.2.1.2.2

Factor $100$ out of $200 K$ .

$V = 100 (3) \frac{0.23 L}{100 (2 K)} K$

Step 3.3.2.1.2.3

Cancel the common factor.

$V = 100 \cdot 3 \frac{0.23 L}{100 (2 K)} K$

Step 3.3.2.1.2.4

Rewrite the expression.

$V = 3 \frac{0.23 L}{2 K} K$

Step 3.3.2.1.3

Combine $3$ and $\frac{0.23 L}{2 K}$ .

$V = \frac{3 (0.23 L)}{2 K} K$

Step 3.3.2.1.4

Multiply $0.23$ by $3$ .

$V = \frac{0.69 L}{2 K} K$

Step 3.3.2.1.5

Cancel the common factor of $K$ .

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Step 3.3.2.1.5.1

Factor $K$ out of $2 K$ .

$V = \frac{0.69 L}{K \cdot 2} K$

Step 3.3.2.1.5.2

Cancel the common factor.

$V = \frac{0.69 L}{K \cdot 2} K$

Step 3.3.2.1.5.3

Rewrite the expression.

$V = \frac{0.69 L}{2}$

Step 3.3.2.1.6

Factor $0.69$ out of $0.69 L$ .

$V = \frac{0.69 L}{2}$

Step 3.3.2.1.7

Factor $2$ out of $2$ .

$V = \frac{0.69 L}{2 (1)}$

Step 3.3.2.1.8

Separate fractions.

$V = \frac{0.69}{2} \cdot \frac{L}{1}$

Step 3.3.2.1.9

Divide $0.69$ by $2$ .

$V = 0.345 \frac{L}{1}$

Step 3.3.2.1.10

Divide $L$ by $1$ .

$V = 0.345 L$