Q. 3.17 - An Introduction to General, Organic, and Biological Chemistry

Question

Calculate the unknown temperature in each of the following:

a. ${37.0}^{\circ }\mathrm{C}=\_\_\_\_\_\_\_ °F$

b. $67.3^{\circ }F=\_\_\_\_\_\_\_ °C$

c. $-{27}^{\circ }\mathrm{C}=\_\_\_\_\_\_\_ °K$

d. ${62}^{\circ }\mathrm{C}=\_\_\_\_\_\_\_ °K$

e. ${114}^{\circ }F=\_\_\_\_\_\_\_ °C$

Step-by-Step Solution

Answer

a. ${37.0}^{\circ }\mathrm{C}=98.6 °F$

b. $67.3^{\circ }F=18.5 °C$

c.  $-{27}^{\circ }\mathrm{C}=246 K$

d.  ${62}^{\circ }\mathrm{C}=335 K$

e. ${114}^{\circ }F=46 °C$

Step 1: Given Information (a)

(a) The unknown temperature of  $37.0°C$

Step 2: Explanation (a)

The smaller units by which the temperature difference with the freezing $(0°C)$ and also the boiling points  of water $(100°C)$are divided are called degrees.

Let us determine the conversion of $\left({37.0}^{\circ }\mathrm{C}\right)$ to ${}^{\circ }F$ . 

The factor is as follows:
$T_{\mathrm{F}}=1.8\left(T_{\mathrm{C}}\right)+32$

$T_{\mathrm{F}}=66.6+32$

$T_{\mathrm{F}}={98.6}^{\circ }\mathrm{F}$

Therefore, we have

${37.0}^{\circ }\mathrm{C}={98.6}^{\circ }\mathrm{F}$

Step 3: Given Information (b)

(b) The unknown temperature of $67.3°F$

Step 4: Explanation (b)

(b) we've got to see the conversion of $(65.3°F)$ into $°C$ . The factor is as follows:
$T_F=1.8\left(T_{\mathrm{c}}\right)+32$
Substitute the Fahrenheit temperature within the equation.

$65.3=1.8\left(T_{\mathrm{c}}\right)+32$

$1.8\left(T_{\mathrm{c}}\right)=65.3-32$

$T_{\mathrm{c}}=33.3$

$T_{\mathrm{c}}=\frac{33.3}{1.8}$

$T_{\mathrm{c}}=18.5°C$

Therefore, we have

$65.3°F=18.5°C$

Step 5: Given information (c)

(c) The unknown temperature of $-27°F$

Step 6: Explanation (c)

(c) Determine the conversion of $-27°F$ into $K$. The factor is as follows: 

$T_k=T_{\mathrm{c}}+273$

Substitute the Celsius temperature within the equation. 

$T_k=-27+273$

$T_k=246 K$

Therefore, we have

$-27°F=246 K$

Step 7: Given information (d)

The unknown temperature of $62°C$

Step 8: Explanation (d)

(d) Determine the conversion of $62°C$ into $K$. The factor is as follows: 

$T_k=T_{\mathrm{c}}+273$

Substitute the Celsius temperature within the equation. 

$T_k=62+273$

$T_k=335 K$

Therefore, we have 
$62°C=335K$

Step 9: Given Information (e)

The unknown temperature of $114°F$

Explanation (e)

(e)  Finally, we've to see the conversion of $114°F$ into $°C$. The factor is as follows:

$T_{\mathrm{F}}=1.8\left(T_{\mathrm{C}}\right)+32$

Substitute the Fahrenheit temperature in the equation

$114=1.8\left(T_{\mathrm{c}}\right)+32$ 

$1.8\left(T_{\mathrm{c}}\right)=114-32$

$1.8\left(T_{\mathrm{c}}\right)=82$

$T_{\mathrm{c}}=\frac{82}{1.8}$

$T_{\mathrm{c}}=45°C$

$\cong {46}^{\circ }\mathrm{C}$

Therefore, we have

${114}^{\circ }\mathrm{C}={46}^{\circ }\mathrm{C}$