Chemistry Examples

$2.5 M \cdot V = 1 \cdot 0.5$

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.

$\frac{(P) (V)}{T} = \frac{(P) (1 \cdot 0.5)}{T}$

Step 3

Solve for the unknown.

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Step 3.1

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$V (V) = V (1 \cdot 0.5)$

Step 3.2

Simplify $V \cdot 1 \cdot 0.5$ .

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Step 3.2.1

Multiply $V$ by $1$ .

$V \cdot V = V \cdot 0.5$

Step 3.2.2

Move $0.5$ to the left of $V$ .

$V \cdot V = 0.5 V$

Step 3.3

Subtract $0.5 V$ from both sides of the equation.

$V \cdot V - 0.5 V = 0$

Step 3.4

Factor $V$ out of $V \cdot V - 0.5 V$ .

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Step 3.4.1

Factor $V$ out of $V \cdot V$ .

$V (V) - 0.5 V = 0$

Step 3.4.2

Factor $V$ out of $- 0.5 V$ .

$V (V) + V \cdot - 0.5 = 0$

Step 3.4.3

Factor $V$ out of $V (V) + V \cdot - 0.5$ .

$V (V - 0.5) = 0$

Step 3.5

Divide each term in $V (V - 0.5) = 0$ by $V - 0.5$ and simplify.

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Step 3.5.1

Divide each term in $V (V - 0.5) = 0$ by $V - 0.5$ .

$\frac{V (V - 0.5)}{V - 0.5} = \frac{0}{V - 0.5}$

Step 3.5.2

Simplify the left side.

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Step 3.5.2.1

Cancel the common factor of $V - 0.5$ .

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Step 3.5.2.1.1

Cancel the common factor.

$\frac{V (V - 0.5)}{V - 0.5} = \frac{0}{V - 0.5}$

Step 3.5.2.1.2

Divide $V$ by $1$ .

$V = \frac{0}{V - 0.5}$

Step 3.5.3

Simplify the right side.

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Step 3.5.3.1

Divide $0$ by $V - 0.5$ .

$V = 0$