Answer:
38.3 miles
Explanation:
First, we <u>convert 1.95 gallons to mililiters</u>:
- 1.95 gallons * = 7380.75 mL
Then we <u>calculate how many grams of octane are available for the reaction</u>, using its density:
- 0.6916 g/mL * 7380.75 mL = 5104.53 g C₈H₁₈
Now we <u>convert octane grams into octane moles</u>, using its molar mass:
- 5104.53 g C₈H₁₈ ÷ 114 g/mol = 44.78 mol C₈H₁₈
Then we <u>calculate how many kJ are produced from the combustion of 44.78 mol C₈H₁₈</u>, <em>if 2 moles produce 10900 kJ</em>:
- 44.78 mol * 10900 kJ / 2 mol = 244032 kJ
We<u> calculate how many seconds is the car available to keep going</u>, <em>if it spends 115 kJ per second</em>:
- 244032 kJ * 1 s / 115 kJ = 2122.02 s
We convert seconds to hours:
- 2122.02 / 3600 = 0.59 hours
Finally we calculate the distance:
- 65 mi/hour * 0.59 hour = 38.3 mi
Think about it this way: a cell can only take in materials through the cell membrane. Naturally, as the cell membrane surface area increases, then the amount of material that can enter the cell increases due to more entry points along the membrane. However, when the cell increases in size then the volume inside the cell will also increase - more volume inside requires more energy to transport materials around the cell. So, there is a trade-off between the surface area and volume.
<span>As an example, consider a sphere as a cellular model. The surface area of a sphere is </span>
<span>SA = 4*pi*r^2 </span>
<span>while the volume of the sphere is </span>
<span>V = 4/3*pi*r^3 </span>
<span>initially, as a very small cell increases in radius, the surface area will increase at a greater rate than the volume. But as the cell gets bigger there will be a point where the volume increases faster than the surface area. Cells have maximized this ratio through evolution (this is also one reason why we are not single-celled organisms). </span>
<span>Some cells are able to get around this issue to some extent by "folding" the membrane, thus increasing the surface area without affecting the volume by much. </span>
6.00x10^9 Co atoms / 6.022x10^23 Co atoms = 9.96x10^-15 moles of Co