A balloon is filled to a volume of 5.0 102 mL at a temperature of 28.0°C. The balloon is then cooled at constant pressure to a temperature of 1.00 102 K. What is the final volume of the balloon?

the answer i got is v=166.66666667

My question is what is the correct sig. figures of that number.

so 166.66?

170 ml

To determine the correct number of significant figures in the final volume, you need to consider the least precise measurement involved in the calculation. In this case, it is 5.0 × 10^2 mL, which has three significant figures.

When converting from degrees Celsius to Kelvin, we add 273.15 to the initial temperature of 28.0°C:

Initial temperature in Kelvin = 28.0 + 273.15 = 301.15 K

The final volume can be calculated using Charles's Law, which states that the volume of a gas is directly proportional to its temperature (when pressure and amount are kept constant). The equation is:

V1/T1 = V2/T2

Where:
V1 = Initial volume
T1 = Initial temperature in Kelvin
V2 = Final volume
T2 = Final temperature in Kelvin

Substituting the given values into the equation:
V1 = 5.0 × 10^2 mL = 500 mL
T1 = 301.15 K
T2 = 1.00 × 10^2 K = 100 K

500 mL / 301.15 K = V2 / 100 K

Solving for V2:
V2 = (500 mL / 301.15 K) * 100 K
V2 ≈ 166.10597 mL

Now, to determine the correct number of significant figures, we count from the leftmost nonzero digit and count all the digits to the right, including trailing zeros (if any). In this case, there are three digits, so the final volume can be expressed with three significant figures:

V2 ≈ 166 mL

Therefore, the correct number of significant figures for the final volume of the balloon is 3.

Two significant digits (volume 5.0 tells you that)