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Chapter 5: Problem 7

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 the gases given off is \(3.0\,kg\). This is calculated using the law of conservation of mass, which states that the total mass of the system remains constant throughout the process. After finding the total initial mass of the grill and charcoal, we subtract the final mass of the grill to find the mass of the gases given off.

Step by step solution

01

Identify the given information

We are given the following: - Initial mass of the grill, \(m_g = 30.0\,kg\) - Mass of charcoal added, \(m_c = 3.0\,kg\) - Final mass of the grill, \(m_{fg} = 30.0\,kg\)
02

Calculate the total initial mass

We need to calculate the total initial mass of the system, which includes both the grill and the charcoal. We can do this by adding the mass of the grill and the mass of the charcoal together: Total initial mass, \(m_{total} = m_g + m_c\) Plugging in the given values, we get: \(m_{total} = 30.0\,kg + 3.0\,kg = 33.0\,kg\)
03

Use the conservation of mass

Since the mass is conserved, the total initial mass should be equal to the final mass: Total initial mass = Final mass of the grill + Mass of gases given off We can now write an equation to find the mass of the gases given off: Mass of gases given off, \(m_{gases} = m_{total} - m_{fg}\)
04

Calculate the mass of gases given off

Plugging in the values in the equation, we find the mass of the gases given off: \(m_{gases} = 33.0\,kg - 30.0\,kg = 3.0\,kg\) So, the mass of the gases given off is \(3.0\,kg\).

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