A0.500 g sample of tnt is burned in a bomb calorimeter containing 610 g of water at an initial temperature of 20.0 celcius. the heat capacity of the calorimeter is 420 j/c and the heat of combustion of tnt is 3374 kj/mol.

(a) write and balance the chemical equation

(b) using these data, calculate the final temperature of the water and calorimeter once the reaction is complete

a) 2C₇H₅N₃O₆ + 7O₂ → 3N₂ + 5H₂O + 7CO + 7CO₂

b) 22.50°C

Explanation:

a) TNT has as molecular formula C₇H₅N₃O₆, and the explosion or combustion reaction produces nitrogen gas, water, carbon monoxide, and carbon dioxide as:

C₇H₅N₃O₆ + O₂ → N₂ + H₂O + CO + CO₂

To balance it, the number of elements must be the same on both sides of the equation. So, first, let's multiply each carbon product by 7, and C₇H₅N₃O₆ by 2:

2C₇H₅N₃O₆ + O₂ → N₂ + H₂O + 7CO + 7CO₂

Thus, N₂ must be multiplied by 3, and H₂O by 5:

2C₇H₅N₃O₆ + O₂ → 3N₂ + 5H₂O + 7CO + 7CO₂

And now O₂ by 7:

2C₇H₅N₃O₆ + 7O₂ → 3N₂ + 5H₂O + 7CO + 7CO₂

b) The calorimeter is an equipment used to calculate the energy released by combustion, and it can be considered isolated. By energy conservation:

Qcombustion + Qcalorimeter + Qwater = 0

The energy released of the combustion must be negative, the signal indicates that the heat is lost. The molar mass of TNT is 227.13 g/mol, thus the number of moles is:

n = mass/molar mass

n = 0.500/227.13 = 2.20x10⁻³ mol

So,

Qcombustion = -3374 kJ/mol * 2.20x10⁻³ mol

Qcombustion = -7.4275 kJ = -7427.5 J

Qcalorimter = C*ΔT, where C is the heat capacity, and ΔT is the temperature variation (final - initial).

Qwater = m*c*ΔT, where m is the mass, and c is the specific heat (4.184 J/g°C).

Thus,

-7427.5 + 420*ΔT + 610*4.184*ΔT = 0

(420 + 2552.24)ΔT = 7427.5

ΔT = 2.5

Tfinal - 20.0 = 2.5

Tfinal = 22.50°C

most historians agree that gabriel mouton, the vicar of st. paul’s church in lyons, france, is the “founding father” of the metric system. he proposed a decimal system of measurement in 1670. mouton based it on the length of one minute of arc of a great circle of the earth (now called a nautical mile, 1852 meters). he also proposed the swing-length of a pendulum with a frequency of one beat per second as the unit of length (about 25 cm). a pendulum beating with this length would have been fairly easy to produce, thus facilitating the widespread distribution of uniform standards. over the years, his work was revised, improved, and extended by a number of french scientists.

the political sponsor of weights and measures reform in the french revolutionary national assembly was the bishop of autun, better known as talleyrand. under his auspices, the french academy appointed several committees to carry out the work of developing a usable system of weights and measures for france. one of the committees recommended a decimalized measurement system based upon a length equal to one ten-millionth of the length of a quadrant of the earth’s meridian (i.e., one ten-millionth of the distance between the equator and the north pole).