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Chapter 11: Problem 27

A balloon of methane gas, \(\mathrm{CH}_{4}\), has a temperature of \(-2.0^{\circ} \mathrm{C}\) and contains \(2.35 \mathrm{~g}\) of the gas. What is the temperature of the gas in Kelvin? How many moles of the gas does the balloon contain?

Short Answer

Expert verified
The temperature of the methane gas in Kelvin is 271.15 K, and the balloon contains approximately 0.146875 moles of methane gas.

Step by step solution

01

Convert temperature from Celsius to Kelvin

Given temperature in Celsius (T_C) = -2.0°C To convert it into Kelvin, we need to add 273.15 to the given temperature. Temperature in Kelvin (T_K) = T_C + 273.15 Let's calculate the Temperature in Kelvin.
02

Calculation of temperature in Kelvin

T_K = -2.0 + 273.15 T_K = 271.15 K Now we have found the temperature of the methane gas in Kelvin, which is 271.15 K.
03

Find the number of moles of methаne gas

To find the number of moles of methаne gas, we will use the formula: Number of moles (n) = mass (m) / molar mass (M) Given mass (m) of methаne gas = 2.35 g Molar mass (M) of methаne gas, CH4 = 12 (Carbon) + 4 x 1 (Hydrogen) = 12 + 4 = 16 g/mol Now, let's calculate the number of moles of methаne gas.
04

Calculation of number of moles of methаne gas

n = m / M n = 2.35 g / 16 g/mol n = 0.146875 moles (rounded to 6 decimal places) Now we have found the number of moles of methаne gas, which is approximately 0.146875 moles. In conclusion, the temperature of the methane gas in Kelvin is 271.15 K, and the balloon contains approximately 0.146875 moles of methane gas.

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Most popular questions from this chapter

A student thinks he remembers reading that if you double the temperature of an ideal gas, its. pressure doubles. He is given a problem where he has an ideal gas at \(25.0{ }^{\circ} \mathrm{C}\) and \(2.5 \mathrm{~atm}\). He is asked what the temperature must be raised to in order to double the pressure to \(5.0 \mathrm{~atm}\). He answers, \(^{\prime \prime} 50.0{ }^{\circ} \mathrm{C}\), of course." Why is he wrong? What lesson should he learn about using the ideal gas law? What is the temperature increase in Celsius degrees that will double the pressure?

Rewrite the ideal gas law solving for \(T\). Also show how all units cancel to leave you with just units of temperature.

A 5.00-L container is filled with \(0.8004\) g of helium gas at \(107.0^{\circ} \mathrm{C}\). What is the pressure of the gas in atmospheres and in millimeters of mercury?

A sample of gas at \(25.0^{\circ} \mathrm{C}\) and \(655 \mathrm{~mm} \mathrm{Hg}\) has a density of \(2.26 \times 10^{-3} \mathrm{~g} / \mathrm{mL}\). What is the molar mass of the compound?

A chemistry student realizes she has forgotten the value of \(R\) and needs to determine it experimentally. She decides to measure the mass, volume, pressure, and temperature of a sample of carbon dioxide gas. She finds that \(4.505 \mathrm{~g}\) of the gas occupies \(2.50 \mathrm{~L}\) at \(23^{\circ} \mathrm{C}\) and \(0.9960 \mathrm{~atm}\). Calculate the value of \(R\) she determines from these data.
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