Question

how many grams in 2.111 x 10^6 ml of iron if the density is 7.874 g/cm^3? the final answer is numerically 1 and the units are 2. a. 2.111 x 10^6 b. 1.662 x 10^4 c. 1.662 x 10^7 d. 1.662 x 10^10 e. 2.681 x 10^5 f. 2.681 x 10^8 g. 2.681 x 10^2 h. g i. ml j. cm^3 k. cm

Explanation:

Step1: Convert volume units

Since $1\ mL = 1\ cm^{3}$, then $V = 2.111\times10^{6}\ mL=2.111\times 10^{6}\ cm^{3}$.

Step2: Use density - mass formula

The density formula is $
ho=\frac{m}{V}$, where $
ho$ is density, $m$ is mass and $V$ is volume. Rearranging for $m$ gives $m=
ho V$. Substitute $
ho = 7.874\ g/cm^{3}$ and $V = 2.111\times 10^{6}\ cm^{3}$ into the formula: $m=7.874\times2.111\times 10^{6}\ g$.
$7.874\times2.111 = 7.874\times(2 + 0.1+0.01 + 0.001)=7.874\times2+7.874\times0.1+7.874\times0.01+7.874\times0.001=15.748+0.7874 + 0.07874+0.007874 = 16.622014$.
So $m = 16.622014\times10^{6}\ g=1.6622014\times 10^{7}\ g\approx1.662\times 10^{7}\ g$.

Answer:

1. C. $1.662\times 10^{7}$
2. H. g