Question 1.33 - Chemistry: Molecular Nature Of Matter And Change

Question

There are $\mathbf{2}\mathbf{.}\mathbf{60}\mathbf{\times }{\mathbf{10}}^{\mathbf{15}}$short tons of oxygen in the atmosphere (1 short ton = 2000 lb). How many metric tons of oxygen are present (1 metric ton = 1000 kg)?

Step-by-Step Solution

Answer

Answer:

 

The weight in kg is $2.355\times {10}^{15}$ metric tons.

Conversion unit of lb to kg

Unit conversions constitute an essential part of calculations and is also termed dimensional analysis. lb can be converted to kg by multiplying with 0.453. 

The conversion unit can be thus written as: 

Converting shorts of tons to lb

$$\begin{gathered} \mathrm{There} \mathrm{are} 2.60\times {10}^5 \mathrm{short} \mathrm{tons} \mathrm{of} \mathrm{oxygen} \mathrm{in} \mathrm{the} \mathrm{atmosphere}. 1 \mathrm{short} \mathrm{ton} \mathrm{is} 2000 \mathrm{lb}; \mathrm{thus} 2.60\times {10}^{15} \mathrm{will} \mathrm{be}: \\ 1 short ton =2000lb \\ 2.60\times {10}^5 short ton = 2000lb \times 2.60\times {10}^5 \\ = 52\times {10}^{17}lb \\ \mathbf{Thus}\mathbf{ }\mathbf{weight}\mathbf{ }\mathbf{ }\mathbf{is}\mathbf{ }\mathbf{52}\mathbf{\times }{\mathbf{10}}^{\mathbf{17}}\mathbf{ }\mathbf{kg} \end{gathered}$$

Converting lb to kg

$$\begin{gathered} \mathrm{There} \mathrm{are} 52\times {10}^{17}\mathrm{lb} \mathrm{which} \mathrm{can} \mathrm{be} \mathrm{converted} \mathrm{to} \mathrm{kg} \mathrm{as}: \\ 1lb = 0.453 kg \\ Conversion factor = \frac{0.453kg}{1lb} \\ Weight in kg = weight in lb \times Conversion factor \\ Weight in kg = 52\times {10}^{17}lb \times \frac{0.453kg}{1lb} \\ \mathrm{On} \mathrm{further} \mathrm{simplification}, \\ Weight = 2.355\times {10}^8 kg \\ 1000kg = 1 metric ton \\ 1kg = \frac{1 metric ton}{1000kg} \\ 2.355\times {10}^8 kg = \frac{1 metric ton}{1000kg} \times 2.355\times {10}^8 kg \\ = 2.355\times {10}^{15} metric ton \end{gathered}$$

Thus the weight in kg is $\mathbf{2}\mathbf{.}\mathbf{355}\mathbf{\times }{\mathbf{10}}^{\mathbf{15}}$ metric tons.