Question

What is the final volume, in L. of a balloon that was initially at 173.8 mL at 17.5°C and was then heated to 78.0*C?

Answer 1

`\boxed {\boxed {\sf 0.775 \ L}}`

Step-by-step explanation:

1. Calculated Final Volume

We are asked to find the final volume of a balloon given a change in temperature. We will use Charles's Law, which states the volume of a gas is directly proportional to the temperature. The formula for this law is:

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

The initial volume is 173.8 milliliters and the initial temperature is 17.5 degrees Celsius.

`\frac {173.8 \ mL}{17.5 \textdegree C}= (V_2)/(T_2)`

The balloon is heated to a final temperature of 78.0 degrees Celsius, but the volume is unknown.

`\frac {173.8 \ mL}{17.5 \textdegree C}= (V_2)/(78.0 \textdegree C)`

We are solving for the final volume, so we must isolate the variable V₂. It is being divided by 78.0 degrees Celsius. The inverse of division is multiplication, so we multiply both sides by 78.0 °C.

`78.0 \textdegree C *\frac {173.8 \ mL}{17.5 \textdegree C}= (V_2)/(78.0 \textdegree C) * 78.0 \textdegree C`

`78.0 \textdegree C *\frac {173.8 \ mL}{17.5 \textdegree C}=V_2`

The units of degrees Celsius cancel.

`78.0 *\frac {173.8 \ mL}{17.5}=V_2`

`78.0 *9.931428571 \ mL= V_2`

`774.6514286 \ mL =V_2`

2. Convert to Liters

We are asked to give the volume in liters, so we must convert out units. Remember that 1 liter contains 1000 milliliters.

`\frac { 1 \ L}{1000 \ mL}`

`774.6514286 \ mL * ( 1 \ L)/(1000 \ mL)`

`774.6514286 * ( 1 \ L)/(1000)`

`0.7746514286 \ L`

3. Round

The original values of volume and temperature have 3 and 4 significant figures. We always round our answer to the least number of sig figs, which is 3. This is the thousandths place for the number we calculated. The 6 in the ten-thousandths place tells us to round the 4 up to a 5.

`0.775 \ L`

The final volume is approximately 0.775 liters.

Answer 2

0.21 L.

Step-by-step explanation:

From the question given above, the following data were obtained:

Initial temperature (T₁) = 17.5°C = 17.5°C + 273 = 290.5 K

Initial volume (V₁) = 173.8 mL

Final temperature (T₂) = 78 °C = 78 °C + 273 = 351 K

Final volume (V₂) =?

V₁/T₁ = V₂/T₂

173.8 / 290.5 = V₂ / 351

Cross multiply

290.5 × V₂ = 173.8 × 351

290.5 × V₂ = 61003.8

Divide both side by 290.5

V₂ = 61003.8 / 290.5

V₂ = 210 mL

Finally, we shall convert 210 mL to L. This can be obtained as follow:

1000 mL = 1 L

Therefore,

210 mL = 210 mL × 1 L / 1000 mL

210 mL = 0.21 L

Thus, the final volume of the balloon is 0.21 L.