Question

A soda bottle is flexible enough that the volume of the bottle can change even without opening it. If you have an empty soda bottle (volume of 2.0 L ) at room temperature (25 C), what will the new volume be if you put it in your freezer (-4.0 C)?1)name the law first2)identify the given , write down the equation and show work

Answer 1

1) Charle's law

2) The new volume at -4.0 °C = 1.8 L

Step-by-step explanation

1) Charle's law

2)Given:

Initial volume of the soda bottle, V₁ = 2.0 L

Initial temperature, T₁ = 25.0 °C

Final temperature, T₂ = -4.0 °C.

The Charle's law equation is:

`(V_1)/(T_1)=(V_2)/(T_2)`

What to find:

The new volume, V₂ at -4.0 °C

Before plugging the values of the given parameters into the equation, the temperature must be converted from °C to K.

T₁ = 25.0 °C = 25 + 273.15 K = 298.15 K

T₂ = -4.0 °C = -4.0 + 273.15 K = 269.15 K

Therefore, to get the new volume, V₂, put V₁ = 2.0 L, T₁ = 298.15 K, and T₂ = 269.15 K:

`\begin{gathered} (2.0L)/(298.15K)=(V_2)/(269.15K) \\ \\ Cross\text{ }multiply \\ \\ V_2*298.15K=2.0L*269.15K \\ \\ Divide\text{ }both\text{ }sides\text{ }by\text{ }298.15K \\ \\ (V_2*298.15K)/(298.15K)=(2.0L*269.15K)/(298.15) \\ \\ V_2=1.8\text{ }L \end{gathered}`

Hence, the new volume, V₂ at -4.0 °C = 1.8 L