Q. 3.18 - An Introduction to General, Organic, and Biological Chemistry

Question

Calculate the unknown temperature in each of the following:

a.  $25°C=\_\_\_\_\_\_\_\_°F$

b. ${155}^{\circ }\mathrm{C}=\_\_\_\_\_\_°F$

c.  $-{25}^{\circ }F=\_\_\_\_\_\_°C$

d.  ${224}^{}K=\_\_\_\_\_\_\_°C$

e.  ${145}^{\circ }\mathrm{C}=\_\_\_\_\_\_K$

Step-by-Step Solution

Answer

a. ${25}^{\circ }\mathrm{C}=77°F$

b. ${155}^{\circ }\mathrm{C}=311°F$

c. $-{25}^{\circ }F=-31.7°C$

d. ${224}^{}K= -49°C$

e. ${145}^{\circ }\mathrm{C}= 418 K$

Step 1: Given Information (a)

(a) The unknown temperature of $25°C$

Step 2: Explanation (a)

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

Let us determine the conversion of ${25}^{\circ }\mathrm{C}$ into ${}^{\circ }\mathrm{F}$. The factor is as follows:
$T_{\mathrm{F}}=1.8\left(T_{\mathrm{C}}\right)+32$
Substitute the Celsius temperature within the equation.
$T_{\mathrm{F}}=1.8\left(25\right)+32$

$={77}^{\circ }\mathrm{F}$

Therefore, the temperature are as follows: 

${25}^{\circ }\mathrm{C}={77}^{\circ }\mathrm{F}$

Step 3: Given Information (b)

The unknown temperature of $115°C$

Step 4: Explanation (b)

Let us determine the conversion of  $155°C$ into $°F$ . The factor is as follows: 

The factor is as follows: 

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

Substitute the Celsius temperature within the equation. 

$T_{\mathrm{F}}=1.8\left(155\right)+32$

$T_{\mathrm{F}}=311°F$

Therefore, the temperature in kelvin are going to be  $311°F$

Step 5: Given information (c)

The unknown temperature $-25°F$

Step 6: Explanation (c)

(c) Determine the conversion of $-25°F$ into $°C$

The factor is as follows: 

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

Substitute the Fahrenheit temperature within the equation. 

$-25=1.8\left(T_{\mathrm{c}}\right)+32$

$1.8\left(T_{\mathrm{c}}\right)=-25-32$

$1.8\left(T_{\mathrm{c}}\right)=-57$

$T_{\mathrm{c}}=-{31.7}^{\circ }C$

Therefore, the temperature in kelvin are $-31.7°C$

Step 7: Given Information (d)

The unknown temperature of $224 K$

Step 8: Explanation (d)

(d) Convert the temperature of $224 K$ into $°C$ as shown below:
The factor is as follows: 

$T_{\mathrm{K}}=T_{\mathrm{C}}+273$

Substitute the Kelvin temperature in the equation

$224=T_c+273$

$T_C=-{49}^{\circ }\mathrm{C}$

Therefore the temperature is $-{49}^{\circ }\mathrm{C}$

Step 9: Given Information (e)

The unknown temperature of $145°C$

Explanation (e)

(e) We must convert the temperature from $145°C$into kelvin. The conversion factor is as follows:

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

Substitute the Celsius temperature in the equation

$T_{\mathrm{K}}=145+273$

$T_{\mathrm{K}}=418 K$

Therefore, the kelvin temperature will be $418 K$