It's a perfectly good question, and there is an answer for the dilemma of God either being purely, vindictively just to the utter neglect of mercy, or His being merciful in such a way as not to violate His own justice, and there is way out in His being consistent in either case, as the Lord is not such a lawyer who succeeds in painting himself inextricably into any corner. He knows His own law well.
In the first case of God sentencing an unbelieving, impenitant and doomed sinner to eternal retribution without any mercy at all being offered, the object might be raised that such a judgment being devoid of mercy is a witness of God's being either unwilling or unable to exert mercy, but that would be a false conclusion for 2 reasons:
#1 God is not under any binding obligation to show mercy as mercy is an unmerited privilege and not an inherent legal right. When a proven murderer is punished for his crime...that is justice, but when one is pardoned...that is mercy because the very structure of mercy is not for one to receive what he deserved, but for one to receive what he did not deserve. So, if a sovereign were to withhold pardon from a known, proven murderer, he is well within his rights as mercy was never something that the convicted criminal ever did have a right to. God can condemn a sinner if He were so to wish, and not be accused of withholding mercy to him because God was never legally bound to in the first place...but,
#2 God also cannot be accused of being devoid of mercy in the just execution of any sinner, for the simple reason that He had already generously granted that sinner mercy, though the expenditure of His mercy was entirely in vain to the sinner's redemption. Mark this well: There are no little babies or small children in Hades, because God covers them all with the unsolicited and universal children's atonement, and this pardon of them is also mercy, as a little sinner doesn't have any inherent right to mercy any more than an old sinner does. So, when a sinner of adult status is sentenced to eternal punishment, none are ever prosecuted in that ghastly place for the sin's of either their conception, infancy, or childhood, because those sins were pardoned as a matter of grace by God unmeritoriously when they were at that age. This is one reason why the damned "weep" in Hades: Because they had been in possession of a salvation of pardon right in their very hands as children, but let it slip neglectingly through their fingers by not choosing while adults to voluntarily exercise faith in Christ the Redeemer.
In the second case of God showing mercy to any sinner, He is by that pardon not setting aside His justice in the least, as He is quite able to punish the guilty sentence of the sinner, (as it were,) to the fullest extent of His violated law, and yet pardon him at the same time! This seeming contradiction to all sanity and logic is where the salvation of Jehovah appears in all of it's grandeur, profound mystery, and beauty together. To fulfill the legal requirement of a sinner against them and yet pardon them mecifully at the same time, God uses the principle of legal union. When a penitant and believing sinner is pardoned, justified and indwelt by the Holy Spirit, this indwelling of God the Holy Spirit constitutes a spiritualized sort of marriage, where the believer and Christ are mystically and legally joined into union, which legal union passes the legal status of either one to the other, while not annihilating the personality or free will of either for that matter. It is an incomprehensible miracle indeed, as Christ assumes the guilty sentence of a believing sinner and absorbs his/her punishment within His past punishment, while the believer rejoices to discover that he or she has now legally become the possessor of Christ's acquired righteousness, which is both penal and preceptive. His past death is considered or reckoned to be their legal death, while His Earthly righteous life is likewise considered to now be their legal righteousness, or what is termed "justification". Because of the spiritual union in the joining of the estates of a believer with his or her Lord, the legal status of Him is declared to be, (or "justified",) ours, even though it was not originally ours. Neat deal...isn't it?
God is perfectly able to be thoroughly just in the pardon of any believing sinner, as He was just in the prosecuting of Christ His Son for our offenses, as we were foreseen in God's omniscience as being ultimately united to Him by faith. "Chosen in Him before the foundation of the world".
He might be "Just, and the justifier of the one who has faith in Jesus". Romans 3:26b
