Afahrenheit and a celsius thermometer are immersed in the same medium. at what celsius temperature will the numerical reading on the fahrenheit thermometer be (a) 49° less than that on the celsius thermometer, (b) twice that on the celsius thermometer, (c) one-eighth that on the celsius thermometer, and (d) 300° more than that on the celsius thermometer?

Answer :

(a) The Celsius temperature will be,

(b) The Celsius temperature will be,

(c) The Celsius temperature will be,

(d) The Celsius temperature will be,

Explanation :

The conversion used for the temperature from degree Celsius to Fahrenheit is:

        ..............(1)

where,

= temperature in Fahrenheit  

= temperature in centigrade

(a) less than that on the Celsius thermometer.

As per question, the equation will be:

     ..........(2)

Now substituting (2) in (1), we get:

The Celsius temperature will be,

(b) Twice that on the Celsius thermometer.

As per question, the equation will be:

     ..........(3)

Now substituting (3) in (1), we get:

The Celsius temperature will be,

(c) One-eighth that on the Celsius thermometer.

As per question, the equation will be:

     ..........(4)

Now substituting (4) in (1), we get:

The Celsius temperature will be,

(d) more than that on the Celsius thermometer.

As per question, the equation will be:

     ..........(5)

Now substituting (5) in (1), we get:

The Celsius temperature will be,

n2(g) + 3h2-> 2nh3(g)   this is the balanced equation

note the mole ratio between n2, h2 and nh3.   it is 1 : 3 : 2   this will be important.

moles n2 present = 28.0 g n2 x 1 mole n2/28 g = 1 mole n2 present

moles h2 present = 25.0 g h2 x 1 mole h2/2 g = 12.5 moles h2 present

based on mole ratio, n2 is limiting in this situation because there is more than enough h2 but not enough n2.

moles nh3 that can be produced = 1 mole n2 x 2 moles nh3/mole n2 = 2 moles nh3 can be produced

grams of nh3 that can be produced = 2 moles nh3 x 17 g/mole = 34 grams of nh3 can be produced

note:   the key to this problem is recognizing that n2 is limiting, and therefore limits how much nh3 can be produced.