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Chapter 3: Problem 9

A new grill has a mass of 30.0 \(\mathrm{kg} .\) You put 3.0 \(\mathrm{kg}\) of charcoal in the grill. You burn all the charcoal and the grill has a mass of 30.0 \(\mathrm{kg}\) . What is the mass of the gases given off? Explain.

Short Answer

Expert verified
The mass of gases given off during the burning process of the charcoal is \(3.0\,kg\). This is obtained by applying the law of conservation of mass, which states that the total mass of objects in a closed system remains constant before and after any process. The difference between the initial mass (grill + charcoal) and the final mass (grill + remaining ashes) is equal to the mass of gases given off.

Step by step solution

01

Determine initial mass of the system

Initially, the mass of the system (grill and charcoal) is the sum of the mass of the grill and the mass of the charcoal together: M_initial = M_grill + M_charcoal
02

Calculate the initial mass of the system

Plug in the values of the mass of the grill (30.0 kg) and mass of charcoal (3.0 kg) into the equation: M_initial = 30.0 kg + 3.0 kg M_initial = 33.0 kg
03

Determine the final mass of the system

After burning all the charcoal, the question states that the mass of the grill is still 30.0 kg. As there is no charcoal left, the final mass of the system (grill and remaining ashes) is equal to the mass of the grill: M_final = M_grill M_final = 30.0 kg
04

Apply the law of conservation of mass

The law of conservation of mass states that the total mass of objects in a closed system before and after any process remains constant. So, the difference between the initial mass and the final mass should be equal to the mass of gases given off: M_gases = M_initial - M_final
05

Find the mass of gases given off

Substitute the values of M_initial (33.0 kg) and M_final (30.0 kg) in the equation: M_gases = 33.0 kg - 30.0 kg M_gases = 3.0 kg Therefore, the mass of gases given off during the burning process of the charcoal is 3.0 kg.

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