Question

if the atmosphere currently contains approximately 5.0 × 10^17 kg of co₂, how long will it take for the worlds fossil fuel combustion to double the amount of atmospheric carbon dioxide? when calculating this answer, do not round any values in your calculations until the end when you are reporting the final value. express the number of years to two significant figures.

Explanation:

Step1: Identify necessary data

We are only given the current amount of $CO_2$ in the atmosphere, but no rate of fossil - fuel combustion (amount of $CO_2$ added per year). Without this rate, we cannot calculate the time. Assume the rate of fossil - fuel combustion adding $CO_2$ to the atmosphere is $r$ (in kg/year). The amount of $CO_2$ we want to add is $\Delta m=5.0\times 10^{17}$ kg (to double the current amount).

Step2: Use the formula for time

The formula for time $t$ in terms of mass and rate is $t = \frac{\Delta m}{r}$. Let's assume a common - cited rate of fossil - fuel combustion adding $CO_2$ to the atmosphere of $r = 9.0\times10^{12}$ kg/year. Then $t=\frac{5.0\times 10^{17}\text{ kg}}{9.0\times 10^{12}\text{ kg/year}}$.

Step3: Calculate the time

Using the rule of exponents $\frac{a^m}{a^n}=a^{m - n}$, we have $t=\frac{5.0}{9.0}\times10^{17 - 12}\text{ years}=\frac{5}{9}\times10^{5}\text{ years}\approx0.5556\times 10^{5}\text{ years}= 5.6\times 10^{4}$ years.

Answer:

$5.6\times 10^{4}$ years