Question

given the data in exercise 115, calculate the energy that must be removed to convert 250. g of substance x from a gas at 100. °c to a solid at - 50. °c. assume x has a molar mass of 75.0 g/mol.

Explanation:

Step1: Calculate the number of moles of substance X

The molar mass of X is not given in the visible part of the problem - but assume molar - mass \(M\) is known. First, convert the mass of substance \(X\) to moles. The mass of substance \(X\) is \(m = 250. g\). The number of moles \(n=\frac{m}{M}\). Since \(m = 250.g\) and assume molar mass \(M\) (not shown in the visible text, but if we assume we know it), \(n=\frac{250}{M}\) mol.

Step2: Calculate the total energy change

The energy change per mole is given as \(75.0\ kJ/mol\). The total energy \(Q\) that must be removed is \(Q=n\times75.0\ kJ/mol\). Substituting \(n = \frac{250}{M}\) into the equation, we get \(Q=\frac{250}{M}\times75.0\ kJ\). If we assume the molar - mass \(M\) of substance \(X\) is known (for example, if \(M = 50\ g/mol\)), then \(n=\frac{250\ g}{50\ g/mol}=5\ mol\).

Step3: Compute the final energy value

\(Q = 5\ mol\times75.0\ kJ/mol=375\ kJ\).

Answer:

If the molar - mass of \(X\) is known, substitute into \(Q=\frac{250}{M}\times75.0\ kJ\) to get the energy value. For example, if \(M = 50\ g/mol\), the answer is \(375\ kJ\)